I think I was reading a lot of the classics at that age. Many have already been mentioned - I could add:
History-ish (some actually historically based, some simply set in that era)
Rebecca of Sunnybrook Farm
Pollyanna (my mom's favorite book, she loves it and recommends it to everyone)
Across Five Aprils
Island of the Blue Dolphins
The Witch of Blackbird Pond (I don't remember this being that horribly sad/scary)
Little House books (Laura Ingalls)
Also- First Farm in the Valley: Anna's Story (Anna Pellowski), which is similar to Ingalls' books, but about a first-generation American Polish family (have not read the rest of the series, as our library only has the first book!).
Anything Louisa May Alcott (An Old-Fashioned Girl, etc.; they're not all as sad as Little Women, which I adored at that age)
Nory Ryan's Song - about the Irish potato famine. It's sad at times but ends well, and good history. Lily's Crossing, by the same author, is also good, about WWII and the lead character, a girl, is a very 'real' kid (compulsively lies at first, for instance).
(And others mentioned by previous posters, like Heidi, which has its very sad parts, but comes 'round so wonderfully in the end)
It's not fiction, but I also loved biographies and autobiographies at that age - especially of Presidents/First Ladies.
Fantasy-ish - we loved The Night Fairy, too, so bear that in mind with these suggestions:
Many good ones have been mentioned - I'd say that if you're not that 'into' fantasy, Madeleine L'Engle's "Wrinkle in Time" quintet is good. Scary at times, but never for long. Science sprinkled in, and Meg is such a nice strong girl character!
Also previously mentioned - To the Mountains of the Moon (Lin) is wonderful. And not as "fantasy," more of a fable feel to the book.
A total princess story with a strong princess (I'm pretty anti-princess): Ivy's Ever After.
Also, The Ordinary Princess (M.M. Kaye), another anti-princess type book
The Hobbit (and Lord of the Rings trilogy), in my opinion, are not the same sort of fantasy as so many of the modern fantasy/sci fi books for kids. Excellent books, and your daughter may like them if you haven't tried them with her. Especially The Hobbit.
Also mentioned above, I know I read The Princess and the Goblin in the fourth grade and liked it very much!
Jenny and the Cat Club - about a club of cats. A fellow Mothering mom recommended it, and it was a fun chapter book to read. Nothing scary!
Contemporary - well, we haven't read a lot of that. How to Eat Fried Worms was a book I loved when I was 3/4 grade and suspect speaks to kids today too (as with the Ramona books etc. but I think those are younger than your dd).... A lot of people talk about Diary of a Wimpy Kid.
I was also reading Jack London, Where the Red Fern Grows, Old Yeller, Bridge to Terabitha, etc. when I was that age - but those books are by and large, sad. I discovered early in my life that I like a good tear-jerker. My 7 year old does not -- all the books I've recommended above, I have either read to her (or she's read), or I am confident that she would be OK with them.
Children of the Longhouse by Joseph Bruchac
The Birchbark House by Louise Erdich
Misty of Chincoteague by Marguerite Henry
The Anne of Green Gables books by L. M. Montgomery
Sarah, Plain & Tall by Patricia MacLachlan
Heidi by Johanna Spyri