As you can see, you're going to get all kinds of opinions. I think the best thing to do would be to talk to your girlfriend to see what kinds of activities her daughter would like.
For what it's worth, I don't think flowers are a bad idea.
I wouldn't do a single rose, but I think a small, springy, cheerful bouquet would be lovely. I would bring your girlfriend maybe a larger version of the same bouquet. It's a really nice gesture & shows your girlfriend's daughter that she is important too. I wouldn't make any big presentation speech or anything (I think that's where it tips into the "cheesy" category); instead, I would just give her the flowers when you pick her & her mother up for the evening.
I think most girls would like flowers - and, even if her 11 year old self might, on the outside, act like it's corny or whatever, I think she'll still be touched that you thought of her & are treating her like a lady.
I actually the idea of flowers better than an edible arrangement. Flowers are very traditional & are given in a lot of different circumstances/situations.