Parent of a DD. my first instinct was no (for the reasons you cited) but after reading it, I'm more on the fence. You can always say "if you still want it done at 18, that's your prerogative." Which is true.
FWIW I got my nose pierced at 16. My parents were horrified, but what can you do? Kids are going to do what they want to do, but I'm assuming your DD is better behaved than I was
