If she winds up liking the Little House on the Prairie series, you might give her Understood Betsy by Dorothy Canfield Fisher next. You can have that one for free (yay!) on Project Gutenberg.
Other books that you can have for free (yay!) on Project Gutenbergthat might interest your daughter now or in the next couple of years:
Anne of Green Gables series (L.M.M Montgomery)
A Little Princess
Little Lord Fauntleroy
The Secret Garden (all by Frances Hodgson Burnett)
Tarzan (and about 10 sequels of varying quality - Edgar Rice Burroughs)
Call of the Wild (Jack London)
Tom Sawyer
The Prince and the Pauper (Mark Twain)
I skipped a grade and I graduated early. I can say it’s not a good idea. Now back to the thread. Just make the books available to her and she’ll read. When I was young I read at at a high level, but I detested fiction. I loved history and text books. I’d be in the 2nd and 3rd grade and I read all about history and I loved newspapers and magazines. I used to spend hours at the library reading old newspapers from WWII. I always, even as a kid been a WWII buff. I think 'cause my parents were in Europe in WWII.
I am big on reading, I think it’s a must for kids, but don’t neglect non-fiction. At that age what she reads isn’t as important as the fact she IS reading and likes it.
I don’t know if she can write yet, but also encourage her to write. If she can’t write yet, get her a small cheap tape recorder. Then have her read a book and then go to the tape recorder and ask her to tell the story differently AS SHE would like to have written it.
This will not only encourage reading but develop her imagination as well.
I came in to recommend the authors: Dick King-Smith, Hilary McKay, Karen Hesse, Jacqueline Wilson and Marissa Moss, and the series: Horrid Henry, Geronimo Stilton, Diary of a Wimpy Kid and the horrible histories/geography and science books.
Someone up-thread mentioned Judy Blume, these are great books, well written and much loved but I would suggest anyone read them themselves before deciding on whether to give them to elementary aged children. They often deal with teenage growing up issues that you may not yet be read to talk about.
Another kinda fun read, if you can find it, is Asterix is a wonderful comic and history lesson. They are about $10 a book no matter where you find them.