Clothes serve a purpose (warmth).
Collars/harnesses serve a purpose (identification).
Shoes serve a purpose (warmth and foot protection).
Even tattoos serve a purpose (identification).
Top knots serve a purpose (keeping hair from irritating eyes).
A stud earring serves no purpose except to fit a person's idea of what beauty should be. Your Yorkie is beautiful already.
I suggest that if you like stud earrings, get another one for yourself. Don't inflict this on your dog.