Actually, many baby girls get their ears pierced in the hospital before they go home. (A family friend, who lives in a foreign country, had seven sons in a row at her small local hospital. The sisters running the place felt so bad that she had no daughters, when her last son was born, they pierced HER ears.)
And an appropriate gift of jewelry for a newborn is a name bracelet made out of beads or a “roita bendele” of thread, stones, or other material.