My daughter turned 7 on Sunday. She is on the same reading level as your daughter I think. Don't know if your school does AR, but she reads in a grade five to six, and completed first grade with 200 AR points. It left me wondering after first grade ended "where does she go now?" I really didn't want her finishing up all the best books before she even entered second grade.
Anyhow, this series has not been suggested and I think she might like it based in what you mentioned. Susan Wittig Albert has a series about Beatrice Potter that's very sweet, around grade 6 AR 13 points each. There are six of them I believe so far. I chose these for my daughter because she had read all Roald Dahl, all the Ramona books, the first three Potters, etc. my daughter likes a series book, and she doesn't like to be frightened.
There are some freebies on kindle that are really good, too. Around the same AR. "The princess and the goblin", "the princess and curdie", and mark twains granddaughter wrote a lovely book called "daddy long legs" that's also free on kindle.
Oh! And the Inkspell series. And wrinkle in time. And... And... I could go on and on like... Have you checked out this list? We have about half of these in ur library right now.
http://www.npr.org/2013/08/05/207315023/the-ultimate-backseat-bookshelf-100-must-reads-for-kids-9-14
