We do this. Except, we are doing it as a mother-daughter book club. The reading level of our group is diverse--we still read chapter books. They are chosen on interest level rather than reading level. By including the mothers, this is possible for us--they can read together or separate.
It has been a lot of fun. During the summer, the mothers and I made the reading list. We met every two weeks or so and tried to tie in an activity with the book. So, our first book was "The Hundred Dresses". After we talked about it, the girls made paper dolls and designed some dresses for them. Sometimes, the girls just play afterwards. Once, we went to a movie (the Ramona movie because we were reading the Ramona books). After the movie, we went to have a snack and discussed book vs movie.
For the "school year" we meet once a month. Some of the girls hs and some go to ps. Either way, our schedules are tighter during the school year. The girls are taking turns choosing a book. Except last month we had all the girls read whatever they wanted and then come back and "booktalk" it. Most girls read two or three that they wanted to share. That was actually one of the best meetings yet because all the girls talked. Sometimes, they all look at each other like "well, we all know what happened" and clam up. To prevent that, we all try to bring a question to ask the others.
Oh, and some months, a girl comes who hasn't finished the book. For us, we don't worry about it. The other girls fill her in and she is still an active part of the group. It is nice to have a relaxed attitude about this because we are doing it to foster a love of reading, have fun discussing books with each other, and to have a great social opportunity for moms and girls. As we get older, I hope the group stays together and we can read some books that will take us into important conversations.
You may like this site--even if you aren't having the mothers involved.
http://motherdaughterbookclub.com/about-2/
Amy