For the first 30 days after birth, healthy newborns have a compound in their system called gamma globulin, which is amazing at fighting infections. I believe that still give people shots of gamma globulin when they travel internationally.
Infants inherit much of their immune system from their mother, so they will likely be prone to the same infections. Breast feeding in the first 6 months is one of the most important factors to a newborn developing a healthy immune system, as breast milk contains necessary antibodies.
Thanks for the wonderful input, much appreciated.