My parents made me wait until my 16th birthday to get my ears pierced. I made my daughter wait until her 12th. She turned 12 last week and we are finally getting her ears pierced this weekend. I will refuse to let her get any other piercings or own a pet until she moves out. Am I only hurting her by doing this ?

As I mentioned on your other thread, remember positive enforcement.
Basically bribery and corruption works..

If she wants something then she needs to earn it.
She wants her ears pierced, then she has to keep her room tidy for a period, THEN she can have it done..
You both win that way..

Well, to be honest, think about why you're not letting her get it. If it's because she's not very mature for her age. Say so. But actually when you go deeper into it you find that there isn't really a reason why not. I'm also 12, and I know how it feels to want something and having thought it through knowing you want it and your parents stopping you (as their job0. But sometimes you just wish you had a little freedom. I got my ears pierced at about 1-2 years old. Going to get my 2nd holes and maybe cartilage and I'm 12 now. Some people our age already have LOADS of piercings. Test your daughter. See if she REALLY wants it or if she's just following the crowd. Personally, I'm not the type of person who really cares what others think, but some people are just crowd pleasers. Anyway what I'm getting at is see if she really wants it before 16/18, if she does, you need to think why you're not actually letting her. Also, some people just aren't the piercing kind, but if she is, then I think this answer will help from someone who gets it!
Good luck xx

I don't understand how refusing to allow her to get multiple piercings and/or have a pet will "hurt" her.

It's your job to parent the best way you know how. I don't know any adults who have permanent emotional (or physical) damage from being denied piercings and/or pets.

Sometimes "no" is the answer.