Wow, I wasn't even aware doctors pierced ears... ever.
I've worked at the mall piercing ears and am a certified body piercer as well, so I *should* be able to help you with this problem.
Unfortunately, I can't. If someone brought a baby to me in a piercing shop and asked me to pierce their ears, I would have declined, simply because it's done with a hollow needle and the process is much more long and drawn out than in the mall. I'd recommend going to, say, a Claire's to get it done because the process is quick and easy, but it'd have to be a Claire's with an awesome manager that had OCD when it came to germs like I do. I definitely don't recommend those piercing kiosks.
Maybe head to a Claire's and find out when the store manager is working. I wouldn't let a sales associate do it.
Make sure she can hold her head up just fine by herself before you take her (not sure exactly how old she is). That way, the muscles in the neck are defined enough to pop her ears out, away from her head. You have less scarring like that.
Good luck.