We got our son's first passport at 11 weeks, so I feel the OP's pain.

Helpful hints:
-To take a passport photo for an infant, spread out a plain blanket on a convenient horizontal surface (e.g. the floor), place infant on back on blanket. Stand over infant pointing camera down and spend several minutes making noises until you have a photo where they're looking at the camera, both eyes are open, hands aren't in mouth, etc.
-There are extra requirements for getting passports for minors. Be prepared.