C.A.
I personally would not pierce my baby's ears. It is a decision I would leave to my little girl. I didn't have my done until I asked for it when I was about 10 years old. My mom went over the pros and cons (risk of infection, care, etc) with me and let me decide. When I decided to do it she took me to have it done and then took me out to dinner without my brothers. It is one of my special "girl" memories I have with my mom.
I don't necessarily see anything wrong with a little girl having her ears pierced, I just don't think it is necessary. I'm also hesitant to put holes in someone else's body without their informed input and at 2 1/2 I don't think she really understands. She is just saying what Daddy and Grandma want her to.
Good Luck.