I'm neither yes or no. I'm so for piercings, having had several, and still have a few, myself. I've had my tongue and my nose done, both came out though. My tongue was due to it being part of the accident that broke my front tooth. And the nose, an itsy bitzy little stud, got caught on a blanket and ripped my skin away from the tissue in my nose, very painful, and I could not get it back in. My tongue did not scar, actually tongues aren't supposed to scar. My nose however, did have a small bump for many years, I can't see it now but can still feel where it used to be.
The other thing to consider, is that if your daughter wants to get a job when she turns 16, she's going to find alot of people won't hire her with a facial piercing. Or they'll ask her to remove it, and that's just an annoying process. When I was working, I had a boss who hired me because we had a similar tattoo, but when she saw my tongue ring a few weeks later, stated she wouldn't have accepted me if she had seen it before.
On top of that, it wasn't until I was 18 before I got my first piercing, my navel, which that too had to come out when I was pregnant and had surgery. My last two piercings I won't mention, but they are living happily and causing me no problems, yet. lol
My point is, yes, piercing are cool, at a certain age, but then the novelty wears off for most people. I'm only 28, and realizing that what was considered cool only a short 10 years ago, doesn't really fit in my adult life.
Sorry I couldn't give you a more yes/no black/white answer, all I can offer is my experience living with piercings. Loved them at first, kinda wish I had the foresight I have now, still cool to live outside the norm though. Good luck, and happy birthday to your daughter.