Your immune system cannot tell the difference between "natural" immunity caused by exposure to the live disease, and "unnatural" immunity caused by exposure to the dead disease. I made sure my son built up his immunity by exposing him to inactivated viruses and parts of bacteria. Not only is he immune, but he never had to suffer a horrible, potentially life-threatening, brain-damage inducing disease to become immune.
Considering some kids get encephalitis and side effects, even death after the vaccination, I’d say you’re both lucky.