I had my daughter's ears pierced when she was 11 months. I had the folks at Icing at Claire's (Valley Fair Mall, San Jose) pierce her ears because my daughter's pediatrician does not pierce ears. They were very professional. You can ask them questions about their piercing methods. I believe they cost about $30-$35. Make sure you ask for 14K gold or a higher karat of gold.
I saw the comment about having your daughter make her own choices. That is up to your best judgment. I think ear piercing is a personal and cultural choice. In my culture and the home country, girls ears are pierced at birth. We believe that it's better for girls to have their ears pierced when they do not remember rather than experience the pain when they are more grown up.
I saw a stark difference between ear piercing attitudes in San Jose versus Columbia, Maryland (near Baltimore). When I had my daughter's ears pierced in San Jose, the passers by did not really care too much about it. However, when one of my daughter's piercings closed up (at 13 months) and I had to do it again out-of-state, passers by made a spectacle of it. They stop and stared at her and said things like, "Poor baby!" The moms asked me questions about when my ears were pierced and how I came to the decision of having my daughter's ears pierced. I just told them my attitudes towards ear piercing in my culture (such as helping people distinguish between a girl and boy) and how I believe earrings make a girl look dainty. ;)
Let us know what you decided to do and best wishes to you and your daughter.