Your doctor should be able to pierce your baby's ears for you, at least your doctor should be able to tell you where you can get them pierced. Here are some safety guide lines that you may find useful as well.
Infection is probably your worse fear. A poorly sterilized needle may cause infection, or just getting dirt in the open sore. Make sure you clean the ear with rubbing alcohol, and contact your doctor if it swells or leaks pus. While the person piercing your child's ears won't care too much about what you're going to do afterwards, they may care if the child has had tetanus shots. See your doctor first and make sure your child has the appropriate shots.
Another reason to see your doctor before getting your child's ears pierced is to determine if your child is allergic to any metals. If you pierce your child's ear with gold or silver they may have a reaction, you don't want to have to take the earring out early.
You'll also have to ensure your child is careful with their earrings; they don't want to catch them on anything while running at full speed.
Last but not least, don't pierce your baby's ears with a piercing gun. The damage to the cartilage in your ear is much more severe with the violent action of a piercing gun. A professional should use a needle; it's less painful and will look better in the long run.
