Fablehaven by Brandon Mull.
Anything Tamora Pierce; I'm partial to the Circle of Magic but you could start her in Tortall just as well.
His Dark Materials by Philip Pullman.
Enchanted Forest Chronicles by Patricia C. Wrede.
Ella Enchanted by Gail Carson Levine.
Sophie's World by Jostein Gaarder
Sharon Shinn (not arbitrary books, some of them have a touch of adult content, particularly avoid Wrapt in Crystal and Heart of Gold until she's a bit older; I recommend Archangel in another comment and that's a fine starting point but I think Safe-Keeper's Secret and sequels are best optimized for a kid)
Possibly Zenna Henderson. Mix of fantasy and sci-fi flavors but with a very consistent, distinctive aesthetic throughout; if you like one Zenna Henderson story you'll probably like them all. Vaguely religious sentiments, but coated in enough speculative fiction stuff to be even less problematic than Narnia.
I assume she's already read Harry Potter? That, if not.
Watership Down by Richard Adams is good and is about bunnies. I'm really not sure if I'd classify it as "fantasy". I mean, it's about intelligent bunnies, but they just talk to each other and other animals, they don't communicate with humans or do magic or anything. But it's good.
Michael Ende - Neverending Story and Momo are both available in English.
Avoid Piers Anthony. Piers Anthony exists to be the only available speculative fiction with a kid-accessible writing style in libraries run by people with no taste; saturate her with anything but and perhaps she will never be driven to read his crap.
His Dark Materials by Philip Pullman.
Bah ! The first book in the series was great. The second one was ok. The third one was what felt like 500 pages of non-stop didactic moralizing. In the unlikely event that I ever meet Pullman, I would love to remind him that this kind of heavy-handed anvil-dropping didn't work for C.S.Lewis, and it doesn't work for Pullman, either. Bah I say !
Watership Down by Richard Adams is good and is about bunnies.
I read it when I was an adult, and it almost gave me nightmares. It's a great book, don't get me wrong, but...
...
I bought my niece a Kindle that just arrived and I'm about to load it up with books to give it to her tomorrow for her birthday. I've decided to be a sneaky uncle and include good books that can teach better abilities to think or at least to consider science cool and interesting. She is currently in the 4th Grade with 5th coming after the Summer.
She reads basically at her own grade level so while I'm open to stuffing the Kindle with books to be read when she's ready, I'd like to focus on giving her books she can read now. Ender's Game will be on there most likely. Game of Thrones will not.
What books would you give a youngling? Her interests currently trend toward the young mystery section, Hardy Boys and the like, but in my experience she is very open to trying new books with particular interest in YA fantasy but not much interest in Sci Fi (if I'm doing any other optimizing this year, I'll try to change her opinion on Sci Fi).