If that’s her will, yes of course. But I would disapprove. And I might (this is a tough call, and a point where my moral discipline as a parent would probably lack), would be to have her pay for it herself. (I don’t have a daughter, only a son, 1.6 years old, so I’m not there yet.)
My thoughts would be:
There are fights that are worth taking, and there are fights that might be better off unfought.
This doesn’t sound like a real issue worth going into a (possible) conflict for. Besides, you will probably not gain any further ground in the issue, as she’s already made up her mind what she wants, and preventing her from getting that (in this case, really just a harmless piece of jewelry), might only pose a risk for a worse family relation.