My ds7 is very much like your dd. He has been a voracious reader ever since he first learned how to put sounds together. I don’t really give him books related to our subject matter for his free reading time. This is something I plan to start next year when he is 8. I just think it’s a bit too soon for me to assign reading outside of school time. I also do not require narrations of his free reading selections, although I will occasionally ask him what’s going on in his books or what his favorite part has been so far. If he can’t give me a good, thought out answer, I know he’s flying through the book for the sake of turning pages, not for soaking it in and actually learning something.
That said, maybe you could encourage her to read longer books. It sounds to me like “Rainbow Fairies” and “The Puppy Palace” are short picture books, rather than long chapter books that encourage her to really immerse herself in the story. We also have pretty much cut library time out, not because I don’t love the library but because finding too many books was becoming an issue. Not only do we not have the space, but like others, I would much rather they took their time really enjoying one great book than flying through as many books as possible just for the sake of it.
I think suzukimom was wise in asking what else she does in her free time. Is reading it? Is she playing outside? Involved in any extracurricular activities? Helping around the house? Learning life skills? Chores? To give you an example of how our free reading time works: Children wake up and must do their personal devotion first. Then they are allowed to read until 8:30, when they make their bed and get dressed. After breakfast is school time, then they have chores which must be completed before they are allowed to play/read. If this doesn’t happen before lunch, they have to postpone playing and/or reading until after mandatory rest time when chores must then be completed. About two days per week, I will allow them to have quiet reading time in their beds rather than nap/rest. Only after chores, rest, and a snack can they have free reign over their time to read or play. If it’s nice out, I sometimes require them to ride their bikes, sidewalk chalk, or we’ll go on a walk. If too cold or windy, they obviously can read if they choose. I have also discovered that several non-battery operated games are good investments for long afternoons in the wintertime. We enjoy Connect 4, Skip-Bo, Bananagrams, Bingo, and Guess Who?. Then we have supper, family clean up, devotional, and family read-aloud.
Before implementing this schedule, my ds was reading 4-5 hours a day. I didn’t think it was a problem until I realized what you are realizing now. It’s a good problem to have, but like anything, even reading in moderation is wise. 
Blessings,
Lindsey