P.A.
There's a jewelry store on Archer around Kedzie. They did my daughter's when she was 3 months old. Clean, expereinced and sensitive to the anxiety of the young child.
Sorry I don't remembe the name anymore. But also, if your daughter is old enough to want them she should be fine going to the Piercing Pagoda or Claire's at the mall.
Warning: if she has sensitive skin at all, sping for the 14K or better starters, you lessen the chances for infection.
Good luck
ABOUT ME:
Latina Mom who is culturally obligated to pierce ears of girls as early as possible.