I've been reading fantasy since I discovered The Lion, the Witch, and the Wardrobe when I was about 9ish. I'll list out some of the stuff I can recall reading and enjoying. MSJ, you've given me a lot of great books to read, hopefully I can return the favor vicariously for your daughter
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Narnia (Lewis) is for about that age. You can start with Lion, Witch, Wardrobe to get into it, then circle back and read chronologically (book 1 is Magician's Nephew IIRC)
Seventh Tower series by Garth Nix. Lots of magic, people use magic stones charged by sunlight and get magic creatures that take the place of their shadow. Book 1 is The Fall. I think there are 5 books?
Also Nix, Keys to the Kingdom, starts with Mister Monday. I got to old to finish them by the time they got out, but they are a little darker. 7 books maybe?
Series of Unfortunate Events is often cited as a good one for kids too, but I never read them. There's like 13 of these.
Artemis Fowl series by Eoin Colfer. Set in the real world, genius rich kid discovers Faeries live in a hidden world underground. Very fun for the imaginative child. There's probably 6 books now.
Larger books:
The Redwall Series (Brian Jaques) is wonderful fantasy with all the characters being animals. Good guys are usually things like mice and rabbits, the bad guys being rats and the like. Quite fun, and there's a lot of them so you can keep her busy with them. Can be read in any order, though starting with Redwall is probably a good idea as its the title of the series.
I think I read His Dark Materials by Philip Pullman around 12. Brilliant series, highely recommended. Gotta make sure to get some challenging ideas into the young ones, something to purge out Lewis
. Just 3 books, but themes are probably intense for a kid too young. Divorced parents, talks about death extensively in the third book, literally kills god at the end, Christian Church ends up being the Big Bad by the end, her mom is a psycopath... Maybe vet this one before you give it to her. Starts with The Golden Compass.
Actually, set in the same universe is a prequal series called The Book of Dust that begins with La Belle Sauvage. Only the first book is out, but it seemed pretty kid safe, though on the serious side.
Harry Potter is a perfect series to grow up with, which is why its so damn popular. I'd recommend giving her one a year, I think HP starts out as a 12 year old? Perfect . Your daughter can have a summer book for the next 8 years. The books get darker as time goes on, and they get larger, which basically means reading level increases a tad early on. Levels out after they first couple, so once she's 14ish she might want to blast through them all, which at that point is probably fine? No idea - I don't know how kids work lol. - Nevermind, you already mentioned this.
The Inheritance Cycle, starts with Eragon, by Christopher Paolini. Dragons! Who doesn't love dragons. Later books get a bit dark, and they are knockoff amalgamation of standard fantasy tropes, but reads great for kids.
The Legend of Drizzt is probably a bit too adult for now, maybe for later years. By RA Salvatore, there's a lot of fighting and action, magic etc., its published by Forgotten Realms so its essentially D&D in novel form. I probably started reading these when I was 14 and loved them until I discovered Bakker when I was about 18. I wouldn't say they are worth reading as an adult lol, as the writing is mediocre and the plots simple.
Edit:
Oh yeah, and get Calvin and Hobbes. So much great vocabulary in there even as an adult, and its perfect for kids. Buy some used ones from ebay, there's a list of about 12 you can get that will get you every comic out there without overlap. Probably $5 each - no need to get them all at once though.
Added some more.
SciFi is also another option. Ender's Game might be a good place to start out, not sure what age though. 12? I read it as an adult, since I didn't get deep into scifi until much later.
The Giver, which has a series attached to it, is often required reading for 8th grade around here. I read it a few years prior, it might have been what got me into scifi.
I also have to say that probably the only non-fantasy book I can remember reading
and enjoying as a kid was Where the Red Fern Grows. Its an incredible story about a boy and his dogs, and its the first book that made me cry.