They would be for an 11-year old girl. I started paying $0.12 for comics in 1960, and kept buying through the 80’s until it hit $1.25 but stopped reading them then, although I’ve read Watchmen and The Walking Dead. The only ideas I have are Wonder Woman, because c’mon, Wonder Woman, and iZombie, but I haven’t seen the book, just the TV show, and I don’t know if the Vertigo comic is age appropriate.
It is my understanding that the new Ms. Marvel, featuring a teenaged girl of Muslim descent living in NJ has been getting great reviews.
10 Great Comics for Adolescent Girls: Graphic Novels and Collections
10 Great Comics for Adolescent Girls: Ongoings and Miniseries
Squirrel Girl is also fun if the reader is on board with its lighthearted tone.
Absolutely seconding the new Ms. Marvel. The fourth trade paperback just came out - get her all of them. It is a really, REALLY good comic about a young girl (16) coming to terms with her superpowers and finding a way to balance school, family, and crimefighting.
Captain Marvel is also hella good. It’s more “cosmic” and traditional superhero-y, following the adventures of Carol Danvers in space (she meets up with Rocket Racoon from Guardians of the Galaxy).
She may be a bit young for the violence and the environmental topics, but the manga Nausicaa of the Valley of the Winds ( 7 volumes) by Miyazaki is very good. Two female leads, several female supporting characters, impressive dystopia.
Thanks for the advice. Last I knew, Captain Marvel was male, and I never heard of Ms. Marvel. The link with the 10 Great Comics for Adolescent Girls: Graphic Novels and Collections opened right up with that Spider-Man Loves Mary Jane title, which was extremely off-putting, but it got a lot better after that. I may wait a couple of years for the Miyazaki books.
I’d suggest trying her on manga too. Manga has a much wider variety of material aimed at girls and women, and the more popular series should be available through any decent library, so you two can dip a toe in before committing. Most of the really good shoujo adventure series available in English are aimed at older teens and might not be all that suitable for an 11 year old, but these should be OK:
Japanese takes on the girl superhero:
- Sailor Moon, by Naoko Takeuchi, is a classic, hugely popular for about two decades now (your basic secret-identity monster-of-the-week baddie-defeating team of supergirls, 18 volumes plus two volumes of side stories).
- Shugo Chara!, by Peach-Pit (fantasy, girl acquires magical sidekicks that give her superpowers, 12 volumes); light and fluffy and good for younger readers. Libraries might still have the print volumes but they are out of print; it is available digitally from all the usual suspects.
If she might be interested in female-led adventure stories more generally:
- Kamisama Kiss, by Julietta Suzuki (fantasy, girl accidentally becomes a minor god and has to learn how to handle her godly duties, 18 volumes, ongoing), has a bit more on the romance angle than the first two, but the heroine does a lot of trainee-god magic-slinging do-goodering as well.
- Dawn of the Arcana, by Rei Toma (fantasy, political-intrigue rebelling-against-corrupt-kingdom stuff, 13 volumes): this one might be a little intense on the action front, depending on her sensitivity to violence, although it’s not gory by any means.
- Yona of the Dawn, by Mizuho Kusanagi (fantasy, kingdom is taken over by a political coup, princess has to put together a posse to take it back, 19 volumes) is coming out next year, and the anime was fantastic, so I have high hopes for it. Again, this one is a bit heavier on the action/violence.
Finally, manhua (Korean comics) read left-to-right and can be easier for beginners. Unfortunately there’s not much in the “girl’s adventure” category out in English, but you might try Bride of the Water God, by Mi-kyung Yun (18 volumes, ongoing), which is kind of slow-burning fantasy melodrama with more intrigue than action, but well-written and very pretty.
FYI, iZombie the comic is very, very different from the show, and it’s probably not age appropriate for an 11-year-old.
My 10-year-old loves Lumberjanes and Bandette, both mentioned in the recommended ongoing series link. They’re not superheroes, though. Nimona is also popular —that’s a collection, with the story over.
I’ve recommended before the graphic novel series Zita the Space Girl and The Three Thieves. I think the protagonist of The Three Thieves is going to turn out to be a lost princess or something, but in one of the stories it’s she who rescues a prince.
Not exactly superhero, but Kazu Kibuishi’s series The Amulet (currently up to volume 6 out of 9) is really good.
I highly recommend Amelia Rules! by Jimmy Gownley.
As mentioned above, you can’t go past The Unbeatable Squirrel Girl, which is clever and funny and cool and awesome. And Squirrel Girl is an excellent role model for any 11 year old, boy or girl.
Are you getting floppies (periodical issues) or (collected) trade paperbacks? Actually, you should probably just go ahead and get trades.
(I remember when the female superhero subgenre was basically Wonder Woman and She-Hulk. then it was Wonder Woman, Supergirl, Batgirl, She-Hulk, Dark Horse’s Ghost, and some inconsistent small press stuff. Well, and Birds of Prey. OK, maybe it wasn’t that bad by that point. But it’s actually better than that now. 
)
Um, I’m going to ramble a bit, but the bolded stuff I can generally recommend:
If you haven’t bought comics since they were $1.25, that means you missed Birds of Prey, right? You should be able to find lots of collections of those. (The more recent stuff is a new continuity with new backstories for the characters, and I don’t expect DC to explain that. Their packaging and labelling of their superhero reprints has been shoddy for years.)
I have been buying a lot of female superheroes lately, which I enjoy, because Marvel’s doing a lot better with female characters now.
The numbering on Captain Marvel is a pain, because they started over at #1 when Carol went off into space, but the recent Captain Marvel series was pretty fun at times. And Carol, of course, is the present **Ms. Marvel’**s hero, so that connects. I was buying both, but am cutting back and just sticking with Ms. Marvel right now, on the new stuff. (And everything’s getting renumbered again e_e.)
There was a pretty trippy She-Hulk series about a year ago. The art style was controversial, and the story kind of has to be read as a whole, but it was all right.
The current* **Thor ***is a woman, and the art is very pretty. I haven’t read it, but the most recent adjectiveless X-Men was an all-female team. A-Force is the new Marvel “all-girl” team, but I haven’t read it. (And it just started. Maybe pick up some Runaways trades first.)
Silk is sort of the new version of Spider-Man, if that makes sense. There’s also Spider-Woman, Radioactive Spider-Gwen, and three different “Spider-Man” characters, in Marvel’s attempt to throw as many Spider-themed heroes at the wall and see what sticks -- – but Silk is probably the real successor to classic Spider-Man.
***The Unbeatable Squirrel Girl ***is written by Ryan North of qwantz.com, and…wait, come back…it’s actually pretty fun. I can recommend that.
DC has a rather weird take on Black Canary going right now, and a well-regarded Batgirl revamp, and even a Starfire series. I have loved Black Canary for ages, but right now I’m just buying Starfire myself. I don’t know how strongly to recommend it, since I think it’s largely just playing into my love of the Florida Keys setting (and it’s not very densely paced, and kind of male-gazey, I think). But it has Atlee from the Terra and *Power Girl *series a while back, and she’s fun (if a bit of a “girl from a boy’s comic”).
DC is also doing a new Prez with a female lead, but that’s (kind of bloody) satire, not superheroes.
Dark Horse did a completely new version of Ghost not long ago, but I’ve only read a few issues and can’t say much as to its quality. They also have the Buffyverse and Lara Croft rights, and some of those might be OK.
Not superhero:
IDW is doing a Jem comic. Not superheroes, but a little bit like. I haven’t read much of it.
As a middle-aged nerd, I personally like Giant Days (YA, uni students, slice-of-life) but it doesn’t quite fit what you asked for. An 11-year-old girl might like it, though, even if it seems like it’s playing to an older audience.
Now, that said, if (big if) you can find some of the stuff CMX brought over from Japan a few years ago, I really like Sakura Tsukuba’s Land of the Blindfolded. I don’t know if they ever translated all of it. In tone, it may be closer to (gah) Twilight than to Ms. Marvel, but I genuinely do recommend it. (I haven’t finished it, though. I don’t know if it gets much darker than the early chapters, but I doubt it.)
That said, I don’t expect that to be so easy to find now. 
Runaways (which was mentioned in one of those lists) is great.
Really new, as in “First issue came out last week,” but Moon Girl and Devil Dinosaur shows a hell of a lot of promise.
Love and Rockets has many great female protagonists, including some superheroines (Penny Century, Comrade 13, Cheetah Torpeda, maybe a couple others). 11 might be a little young, but leave a copy where she can find it and don’t explicitly endorse it.
No? Okay, try an all-girl superhero team like A-Force (all-female Avengers squad) or X-Men from before the last reboot (all-female X-Men squad).
The greatest girl superhero book ever is Leave It to Chance by James Robinson and Paul Smith. It’s about Chance Falconer, a 12-year-old girl whose father is a Dr. Strange-type mystic superhero. She goes off on her own adventures. It’s solidly YA in tone and the art is beautiful.
And there’s a whole “Magical Girl” subgenre of manga comic books, like Mai the Psychic Girl and Sailor Moon.
Hate to be the umpteenth Ms Marvel fan, but it’s so good! It’s the only comic I’ve ever read by the issue. I make my husband pick it up for me when he gets his pull list.
Sailor Moon is appropriate for an 11 year old. Mai the Psychic Girl definitely isn’t (and it’s also aimed at boys, so the protagonist is less “a person who you could be” and more “a person who you could date”). Also, the latter is wildly out of print.
Seconding The Amulet, although it’s not superheroes; you might also try the Castle Waiting series, if she likes fantasy generally.
It’s not very superhero-y, but I would suggest Aqua/Aria by Amano Kozue. It’s about a gondolier/tourist guide lady living a happy life on Mars, in a future Venice-style city.
Nothing ever really happens. It’s just a nice sensation to read.