As with peanuts, the AAP says a parent can introduce eggs to a baby's diet in the first four to six months of their life, when they begin eating solid foods. Fortunately, there are a variety of ways to feed your baby eggs, and they're easy to chew and swallow. Notably, the AAP also says that if a baby is allergic to eggs, they may be unable to receive certain vaccines as well, since eggs are sometimes used in vaccine production.