I strongly disagree. Although I do have grave concerns about foisting society's images of femininity on young girls, this is not about morality. It is about the health and safety children. And while we often rely upon parents to make that determination, there are times when all professionals must make that decision themselves - that's why you are a professional, because you bring your specialized expertise, educational and experience to bear in all matters. Not all parents are good (or informed) parents. Face it, you are required to get more training to be a nail professional than you are required to get to be a parent! I think these kinds of decisions are at the core of the meaning of being a professional.
You should have a standard policy about what the age minimum is for your different services and that should be informed by what you know about your products and services, what your professional associations recommend, what other professionals say (medical professionals, for example) and what your insurance will cover. Moreover, you should keep in mind that the major US nail manufacturers' and cosmetology associations (PBA, NCA and NMC) all say that gel polishes should not be used on children. You'd be hard pressed in the face of that to justify doing it. I think when you take all of that into consideration, gel lacquer should have a minimum age in the area of 14 to 16.