I think that you can pierce the ears at any time (since many cultures pierce soon after the birth).
As for where, I would definitely go to your pediatrician's office. Here is why I say this - I have a sensitivity to nickel and I have read that sometimes people develop the sensitivity if their ears are pierced with studs containing nickel (or maybe even an instrument containing nickel). I cannot wear most earrings for more than an hour or so, unless they contain mostly gold or platinum, or I even sometimes wears surgical plastic earrings (more attractive than they sound). My doctor's office uses Blomdahl products to pierce and I think that they are the best. Having a metal sensitivity is really annoying and if you can avoid it, you'll save your daughter some irritation down the road ( no pun intended :)).
P.S. - I was reading the Blomdahl site and here is what I learned....
"My kids want to have their ears pierced. I have heard that ear piercing can cause nickel allergy. Is that correct?"
Answer:
The ear piercing procedure as such cannot cause nickel allergy. It is the material that some ear piercing earrings are made of which can cause nickel allergy. All ear piercing earrings made of metal contain nickel – more or less - even gold and silver. The only ear piercing earrings that do not contain any nickel (= 0% nickel) are the ones made of Medical Plastic. Therefore we recommend that your kids get their ears pierced with Medical Plastic.
We are not born with nickel allergy. Nickel allergy is a skin contact alllergy which can develop as a result of continuous contact with objects that contain nickel, such as zips, buttons, coins, and jewellery. Ear piercing is a strong contributing factor to the increasing numbers of nickel allergy sufferers. World wide clinical studies have all identified and confirmed ear piercing as a prime risk factor for developing nickel allergy, with as many as 10-30% of all women affected.
Once you have developed a nickel allergy there is no remedy which can cure the allergy. The only solution is to avoid all contact with metals containing nickel. However this can be very difficult because all metals contain nickel, even gold and silver, mostly in the form of impurities. Therefore, there are no metal earrings which are entirely free from nickel.
If you already have pierced ears we recommend that you wear Blomdahl Caring Earrings - earrings developed in consultation with skin specialists.