You CAN pierce her ears since her immune system is capable of warding off ear infections which may arise from ear piercings, but I personally wouldn't. I believe that everyone should have the right to determine what they want to do to their own bodies, so I frown upon any sort of body modification for babies. It's not nice to decide something permanent for your child, even if you are the parent. She might not even want her ears pierced. I would let my daughter decide on her own. http://sg.theasianparent.com/baby-piercings-2/
I guess, you should wait for a little more time, as the kids her age keep moving their hands and she might hurt herself with the stud that you are going to make her wear after that. I got my daughter's ears pierced when she was close to 4. She was very fond of having studs in ears, seeing mine. But I think, do not rush, wait for the time she turns 3 atleast.
It is not advisable as there might be infection if the wound is not taken care carefully. You can wait until your daugther is older says 5 years old and let her decide herself.
I didn't pierce my 7 year old daughter because I want it to be her decision, not mine. She can look pretty still with cute dresses and hair accessories.
thanks