My husband is Mexican, and in his family and other Mexican families, it is very common to see small babies wearing jewelry. I've even seen a 9 month old wearing a ring. I personally think it's a little over the top. I think earrings are alright on a baby, and they look so cute. Many times I've seen them wearing a mini ID bracelet, with their name engraved on it, that fits tightly to their wrist so it won't fall off.
What I think is soooo cute, and if I have a girl someday I will do, is to buy her an Add-A-Pearl Necklace. You buy the necklace and a few pearls, and then each year for her birthday you "add" new pearls. Then, by the time she reaches her wedding day, she's got a beautiful pearl necklace with a lot of meaning behind it. It can get expensive, but you could also enlist the help of other family members to keep it going.