Let's remember to keep things spoiler-free for the second and third books since some people may not have read them yet
I agree that Rose definitely has her "young" moments - I'm hoping that as the books go on we see a change in that, and I think we will since it is a Young Adult series and a lot of books in that category involve the growth of the main character from child to adult (at least in my experience). I like the contrast we see between Rose's regular teen side and her guardian side, and the struggle it creates within her as far as wanting to do regular teen things but also needing to grow up fast because soon she will be a full-time guardian and her life won't be all hers anymore.
As far as the writing, I guess since it's from Rose's point of view, I expect it to be not as mature as it would be in the third person POV.
I really appreciate the struggle Mead writes in Rose - between her guardian duties but also wanting to be a teen, as well as the entire "blood whore" concept and the thoughts Rose has about that...it kind of amazes to think of someone so young having to deal with those issues and handling them pretty well for how young she really is.