That is a tough one. Though most societies are getting better at being more respectful of different lifestyles, there is still a huge wall of "us vs. them" mentality out there that would be really hard for a little kid to bear I think.
May I ask what her first name is?
I'd probably use
Gayle myself - it's in there, and very close in sound. It doesn't seem fair, and it isn't, but unless you are the kind of person who wants to train their children to be crusaders for a cause right from the get-go, I'd sidestep that whole thing.
If you did want to use it though, for some reason I really like the idea of pairing it with a really whimsical Medieval type name; I guess to heighten the old meaning of the word gay? Like
Guinevere Gay. Or maybe a Jazz-ager, like
Ruby Gay?