My DD was crazy for the Nancy Drew series from around age 7. The original series. She detests the newer version that has been modernized and is more teeny-bopper, and the writing isn't good, so the reader has solved the mystery before Nancy Drew does. She got her American Girl doll when she was past the reading level for the books so she didn't get into those. She also started reading the Harry Potter series around that age.
Mrs. Piggle Wiggle is great fun.
E.B. White's "Charlotte's Web"
Roald Dahl, "James and the Giant Peach", "Matilda", "The BFG" and others.. look for a boxed set at the bookstore!
"A Little Princess" -- The story was made into a film, with young Shirley Temple playing Sarah Crewe. Watching the movie together could be a bonus after the girls read the book! (I don't know how true to the book the movie was, but it's fun to watch anyway.)
"The Frog Princess" series by E.D. Baker (8 books) is one my DD has read over and over even though her reading ability outleveled it long ago, just because she enjoys the story.
"The Unicorn Chronicles" by Bruce Coville says right on it "RL5" which I take to mean 5th grade. He also compiled a collection by other authors called "A Glory of Unicorns".
the "Phantom Stallion" series by Terri Farley, for ages 10+
Bill Wallace has several books about dogs for ages 8-12, such as "Pick of the Litter"
e.l. konigsburg "From the Mixed-up Files of Mrs. Basil E. Frankweiler" ages 8-12
"Mrs. Frisby and the Rats of Nimh" by Robert C. O'Brien, for ages 8-12 -- later adapted to film as "The Secret of Nimh" (The book is always better)
"Confetti Girl" by Diana Lopez is about a middle-school aged girl whose mother has died, and her father, an English teacher, reads a lot. I haven't read it, it may be a little mature for a 7 yr old, but you may want to give it a look.
Gail Carson Levine's "Ella Enchanted", and "Ever"
Tolkien apparently took inspiration for "The Hobbit" from George MacDonald's "The Princess and the Goblin".
The Chronicles of Narnia
Madeleine L'Engle's series (which has a fourth and fifth book I didn't know about until recently!) I read the first three thinking it was a trilogy, years ago, and bought the boxed set of 5 for nostalgia. They are labeled as late fifth grade-sixth grade for reading level.
"Island of the Blue Dolphins" was part of our 4th grade homeschool curriculum, so we got to read it together, and I enjoyed the story again.
**All credit to my DD(14) who has been pulling books off her bookshelves in her room and telling me all about them while encouraging me to make this list, which would have gone on even longer if I'd let her keep going! She's always been an advanced reader and LOVES to read (like me), and just doesn't understand classmates who must be forced to read for school.