I didn’t know they made it into a movie. Now I’ll have to see if Netflix has it.
StG
I really liked Emergence by David R. Palmer. It’s a dystopian future tale about the world after a disease has killed off 99% of mankind. One of the few survivors and the heroine is an eleven year old girl, who has a pet parrot. It’s written in a unique, shorthand kind of style. I could read this one again, if I could only find it.
Ah, but perhaps stranger in a strange land (the e.e. cummings novel) is. 
Dick is an acquired taste, and I say that as a long-time fan. Maybe A Scanner, Darkly would be easier to take, seeing as how it’s based on a true story (and not a pink laser God-thing true story, either).
I’m surprised nobody’s mentioned The Giver yet, but I came in to suggest some old-fashioned Cold War post-apocalyptic novels. Earth Abides is a good one, in that it’s focused on a plague-caused apocalypse (it isn’t yet another nuclear holocaust) and it’s more focused on the society than most of these apocalypse survivor novels are. But to get a handle on just what people were afraid of, you should look up When The Wind Blows, a harsh, uncompromising look at a limited nuclear war and the aftermath.
And no one’s mentioned Stephen King’s The Stand.
StG
Oryx and Crake is pretty sci-fi and pretty dystopian, although it has some dark content that I am sure not all parents of 14-year old girls would approve of their daughters reading. It is also more of a straight-up story (as opposed to Fahrenheit 451, 1984, etc… which are all dripping in socio-political commentary and subtext). If she likes a good yarn with no profound subtext, and wouldn’t be put off by side-stories involving paedophilia, then that might be for her.
The Road is about as dystopian as it gets, although while ‘futuristic’ it is only nominally sci-fi. The Road is one of those stories that affected me for a good while after reading it, as it brutally demonstrates how fragile society and humanity really are.
A more gentle option would be Exodus - it is written for teenagers (and has a 15-year old girl as the protagonist), and only faintly touches on risque themes. There is a lot of topical relevance too (global warming, refugees, etc…). If she is already hooked on hard ‘adult’ sci-fi, this might be a little tame, though.
If she’s willing to read about a society on the edge of becoming a dystopia but isn’t quite there yet, Cory Doctrow’s Little Brother and it’s sequel (third book coming soon) are there. It’s not quite a dystopia yet, but it’s so very close. It’s also great.
I’d also recommend Wool by Hugh Howey.
Should be right up her alley. Post apocalyptic dystopia, strong heroine and a great story. Adult without anything graphic. I loved it.
I agree so much I said so ten posts ago! 
stranger may not be as dystopian as others listed, but its one of the best and most important novels ever written. most of the other books mentioned would never even exist without it.
as derleth says, dick may take some time to get into but electric sheep is not weak, and comparing it to blade runner is not apt as the movie just used the book as a starting point!
and, no matter how you feel about rand (and i have mixed feelings) the importance of her work in american culture cannot be dismissed. and anthem is a pretty fun read.
mc
and every phone rubber should read terminal man by michael crichton
mc
The Enders Game where actual children murder each other?
I’d suggest The Postman by David Brin, A Canticle for Leibowitz by Walter M Miller, and some of H Beam Piper’s short stories.
Also, Ready Player One by Ernest Cline is excellent too - I would have loved it when I was 14.
cite?
Okay, maybe not “weak” but very, very, very, very, very, very, very, very dated.
To an already impressive list, I’d add Max Hasting’s World War Z, a ‘reporters-eye view’ of the Zombie Apocalypse. Written in interview style, it has some strong female characters and a world-wide outlook, and should be accessible to a 14 year old mind without being too depressing.
ok. IMHO, but i’m not alone. from wiki:
mc
If I might be permitted a slight off-topic remark here, but I’ve never understood why Stranger in a Strange Land is seen as this landmark classic. I read it as an adult and was unimpressed; it probably would have bored the hell out of 14 year old me.
I’m with you on this. I didn’t read SiaSL until when I was a freshman in college and the expanded edition was published in 1991. It was an okay SF book, but doesn’t stick out from any number of other SF books I’ve read. Really, it’s only special significance to me is providing the word “grok”, which I can occasionally trot out (like the word “cromulent”) when I want to signal my nerd cred. I have a hard time believing a book about 1960s hippies meeting a spaceman is going to have much of a relevance to a modern teen.
A lot of great science fiction suggestions, but she might really enjoy The Dark Tower series by Stephen King. More bent toward the fantastical, but there is sci-fi elements, strong dystopian landscapes, and a wonderful cast of characters and storytelling.
I ate the early books up as a teen.
+1 on A Canticle for Leibowitz and a few short stories to recommend. I Have No Mouth and I Must Scream and A Boy and His Dog by Harlan Ellison.
Also, The Cold Equations by Tom Goodwin.
It may be worth looking into A Wrinkle In Time as well, I still enjoy it after all these years.