What she does with her body is her business.
After she's eighteen, maybe, but not as a minor. She would need permission for a tatoo, or a peircing, why not a medical proceedure?
Do you think a minor would want to spend the remainder of her young life, what would be her college years, and what would be her first years in the working world had she not spent her college money on her child, well, raising a child?
I'm with BRTD on this one as well. Tattoos and piercings are also one's own business.
And I would be upset if my child had a tattoo, but it's still his/hers choice. I would simply warn them of what would come if she didn't consider herself to be associated with her tattoo in the future. They got the tattoo, and their only punishment should be having to live that tattoo down.