If you haven’t read it, Anne of Green Gables. I loved that book into adulthood. The sequels aren’t as good, but they’re certainly serviceable, as Marilla would say. 
No fantasy/sci-fi element, though. If that’s dispensable, I’d vote for the historical novels and “American Regional” series written by Lois Lenski.
Well, it’s kind of a stretch, but Anne is very imaginative, and often describes the stories she invents.
I would also recommend:
Whales on Stilts by M. T. Anderson (and sequels). Very funny and smart/tough/brave heroines and a hero. The plot is just what it says in the title.
The Search for Delicious by Natalie Babbitt. A Prime Minister is writing a dictionary. If “affectionate” is your dog, what is delicious? Let’s have the kingdom vote on it! Nothing could possibly go wrong with that idea…
The Wonderful O by James Thurber. It’s about an island where people are forced to stop using the letter o.
I second the recommendation for The Egypt Game. It’s a little bit dated, but it’s a wonderful story.
What about the *Dragonriders of Pern *series by Anne McCaffrey? Dragonflight, Dragonquest, and *The White Dragon *are all quite good. And I haven’t yet met a girl who’s read them and not wanted to Impress a dragon.
My daughter is twelve. She devoured the Warriors books. She recently read and enjoyed “The Girl Who Could Fly.”
I’m reading To Kill A Mockingbird to her. I won’t read to her what she’d read herself - because, why?..she’d read it herself. For me to read to her it has to be something we should talk about while we read, that she wouldn’t read on her own, that I enjoy enough to want to share. And since having Mom read to her, and having that time with me, is something special, I can challenge her a little.
(I’m also very biased against people who read a single genre - I wouldn’t encourage that sort of behavior in my reader daughter…Now, my son who doesn’t like to read, if he found a genre he would read, I’d be happy. But her…she can spread her wings a little).
My niece loved The Apothecary by Maile Meloy. I haven’t read it yet but it seems to be blend of Cold War issues and magic.
It’s about a fifth grade level, though, so it might be a bit too young for your daughter.
With all of these suggestions, I should have enough to read to her until she heads off to college. Now I just have to decide which one to try first.
Also, the desire for sf/fantasy elements is more from my side than hers. She has read and enjoyed many novels that are more realistic in tone. She’s read the Ramona books and Anne of Green Gables and Little Women and a bunch of the American Girl books. I just tend to prefer something a bit fantastic in my fiction.
Shannon Hale’s books, especially Book of a Thousand Days, which is really wonderful.
The Lady Grace mysteries by Grace Cavendish. Very short historical mysteries starring a 13 year old ward of Queen Elizabeth I.
Evil Genius, by Catherine Jinks about a genius boy who is destined for greatness, preferably great evil if his teachers have their way.
Alcatraz Versus the Evil Librarians, by Brandon Sanderson.
I have lots of other suggestions that might be more suitable for her individual reading.
The Once and Future King, by T. H. White seems like it would be an good choice. It has all you describe, relaying the story of Arthur, Guineviere, Lancelot, Morgan Le Fey, The Knights of The Round Table, the quest for the Holy Grail, The Lady of The Lake… If she likes it, you can follow up with The Book of Merlin. Wonderful stuff. I was turned onto it by my 13-year-old girlfriend when I was year older.
All Daniel Pinkwater’s books are excellent The Snarkout Boys books (The Snarkout Boys and the Avocado of Death and The Snarkout Boys and the Baconsburg Horror) are one possibility. Another is a series of his books without a standard series name. This consists of The Neddiad, The Iggysey, and Adventures of a Cat-Whiskered Girl. I call it the Ancient Epic series. Borgel and Lizard Music are a couple of other first-rate novels by Pinkwater.
There’s a sequel to Holes by Louis Sachar called Small Steps.
I read the crap out of John Bellairs when I was her age. His most famous book is probably The House With A Clock In Its Walls and if you like his style, he wrote loads of other YA books in it.
She (and you) might enjoy The Haunted Mountain, by Mollie Hunter.
I agree with the suggestion to read Holes. Also, there’s a book I loved at that age called No More Dead Dogs. Its about a student who is tired of reading books about a kid whose dog dies. I was having those same frustrations at the time and so the book really spoke to me.
When I was your daughter’s age, some of my favorite books were a trilogy from Phyllis Reynolds Naylor: Witch’s Sister, Witch Water, and The Witch Herself. An 11-year-old girl and her friend suspect that her elderly neighbor is an evil witch. They read up about witchcraft and this woman’s history in the town, and find things that seem to point to her being a witch. But they don’t witness a lot of the actual supernatural stuff as it’s actually happening (at least until the end of the third book), which allows the adults to say that there has to be a rational explanation, etc. The protagonist is a great role model as she is intelligent, resourceful and honest, and as a kid I found myself wanting to join the girls on their adventures as they spied on the neighbor, made secret plans, etc.
One possible downside is the portrayal of witchcraft. I once saw a review of one of the books on Amazon from a Wiccan who felt offended that the witch in the story was a bad guy. But I think it’s pretty clear in the book that they are not depicting Wiccans or any actual pagan religion, but rather the broomstick-riding witch of old folklore.
I loved those Phyllis Reynolds Naylor books when I was a kid, but I haven’t seen them in years. Naylor got very famous with her Alice series, though.
John Bellairs is a must-read!!
Pros: The author frequently drops references to Arthurian lore. Anne is simply a hopeless fantasy literature fangirl. The vocabulary of this book is incredibly advanced, and can even be challenging for college students.
Cons: I would say that it has a fairly slow moving plot and is rather poetic and lyrical (e.g. descriptions of scenery that go on and on and on dripping with purple prose), which is something that the OP wanted to avoid, I believe.
If you want to find another book (actually series) in the fantasy realm, what about Phillip Pullman’s His Dark Materials? I would recommend reading it first yourself because it isn’t quite an innocent walk in the park.
Spoilers include some content warnings.
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When we meet her, the 11-ish year old heroine drinks, smokes, breaks and enters, steals, and is described as having a savage mind.
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Her quest is basically to destroy organized religion, which was founded by ancient wizards who are now dying and can no longer wield godlike power, but still want to have throngs of followers.
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There are some fantasy elements that could arguably be intended as surrogates of or her people’s equivalents of puberty or the first sexual experience.
Was going to second, or third, or whatever, Terry Pratchett’s Tiffany Aching books, but that seems pretty well covered.
I enjoyed the first couple of Redwall books by Brian Jaques when I was 'round that age. They get pretty formulaic pretty quick though, so you might want to leave off after the first one.
His Dark Materials is kinda heavy stuff - definitely read for yourself first.
I thought The Once and Future King was pretty dry stuff when I read it as an adult, so it might not keep a younger person’s interest.
I was coming in to mention Brian Jacques’ Redwall series, too. They’re definitely inspired by Watership Down. I read 4 or 5 when I was about her age, but I think there are a lot more…
I also enjoyed David Eddings’ Belgariad series, and have re-read it many more times. Plenty of magic and humor there, but some definite whining from the protagonist.