If the state board in your area allows it, I would request a written consent from her parent and that the parent be present, not in the room of course, but in the waiting room.
I've not heard of any state disallowing Brazilian waxing services under a certain age. That would be a new one. I don't think it's so much a legal issue as it is an individual "choice" issue. Personally, for me they must be at least 18 to get a Brazilian, UNLESS the parent is requesting the service and is there to sign the consent form. Hope this helps.
Useful information. Though I have already tried it and I have a good experience of it. So would like to suggest it.