You know, maybe I'm wrong, but I think a baby has enough antibodies (or whatever you want to say) from it's mother to help fight sickness when it's born.

If the baby wasn't capable of fighting off sickness, then it'd die almost instantly once born since the bacteria in the air, not to mention from the birth, would attack it. Also take into consideration, the birthing process is more than likely inside a hospital, with sick people spreading their germs in the air.