First of all, how innocent is she, really? Because if her body is changing and she has absolutely no clue how or why, the time for a good book on the subject and a heart-to-heart with you is long overdue! :) Seriously, though -- there are books on how girls' bodies change that are great, and can really help. I don't have any experience with the American Girl one people mentioned (I have a son and no daughters), but it sounds really helpful. You and your daughter are probably going to have to sit down and have a really deep conversation about the things that are happening to her body. She needs to understand that it's normal and positive and good, but that as she grows and her body changes, certain modesty has to prevail.
The idea of the "training bras" made of thin material is a really good one -- they will preserve her modesty and won't make her hot and uncomfortable. If anyone teases or harrasses her for wearing a bra or for developing, particularly boys at school, tell her to report it -- that, in this day and age, is sexual harrassment, and should not be tolerated! And you follow through with the school administration to be sure it's being quashed! (I remember when I was your daughter's age and started wearing training bras -- the stuff the other kids did back then would in no way be tolerated today!!!!!) She shouldn't have to worry that people will tease her.
You don't have to destroy your daughter's innocence or keep her from being a little girl -- but I think you do have to have a really great mother and daughter talk! :)
Good luck to you and all the best to your daughter.
S.