Breastfeeding provides a newborn a lot of antibody protection for several months after birth which is important to protect them until their own immune systems kick in. But the antibodies in the breast milk don't last for more than a few months, you have no protection at all against smallpox unless you were immunized. I don't believe it's really going to take months to get the immunizations, the virus used to make the vaccine can replicate much faster than that, but even if it does, it's not really that hard for people to do their own if they had to.
How do you go about doing your own vaccination?