) You could get her started on the Betsy Tacy books. They are old, and so sweet. They follow Betsy and her best friend from kindergarten age through marriage, and the reading gets harder as the girls age. Great to give as birthday presents each year to match the bday girl's age.
Boxcar Children books were a big hit with my DD at that age too. Also, the first couple books of the Underland Chronicles - Gregor the Overlander is book one. These also age with the main character so the later ones are probably not as good for a 6 y.o.
There is a sweet picture book with a higher-reading-level story called Elsie Piddock Skips in Her Sleep. DD loved it at six and still reads it once in a while.
Also, this is an age when they can get into some nonfiction if there is an area of interest. There are good basic biographies of great women like Helen Keller and Clara Barton, books on the Titanic or Ancient Egypt, that sort of thing.
I'll pop back in if I remember others later.



I'm not sure if these are still available in stores, but your library should have plenty of them - The Babysitter's Club Little Sister books. They were my favorite when I was that age (until about 3rd grade when I started with the actual Babysitter's Club series) - I must have read them all (and I probably own a good 3/4 of them... I think I have the first 100 or so...)
Also, I haven't seen these mentioned, but Amelia Bedeila and the Sweet Valley Kids books (the second-grade version of the Sweet Valley High books - also probably out-of-print but readily available at the library).