Hi, Stef. Well, typically, we don't start kids on solid foods by giving them eggs. Many people are allergic to eggs, and a baby's digestive system is sooooo sensitive that starting him out too young on foods like eggs can actually CAUSE an allergic reaction that the child might not have if he starts eating it when his system is a little more developed, say when he is well over a year old.
Is your child eating other solid foods right now? If you haven't started him yet, the best ones to start with are things like bananas or rice cereal. Then you can move on to other strained fruits and vegetables, and finally strained meats. Introduce only one new food per week or 10-day period to make sure you know which foods to avoid if he has a bad reaction to something.
If you are asking about eggs because you are worried about giving him enough protein, then don't worry. Milk has a good amount of protein all by itself. Babies are built to get most of their nutrition from milk for the first year of life. If your child is graduating from formula to whole milk, though, it could be time to introduce a gentle solid like rice cereal because regular whole milk will not keep him full for very long, and he could end up eating too much because he is hungry too often. I would get some more advice from the pediatrician who advised you about the whole milk.
You can also give the baby formula from a sippy cup, although it will be harder to get through the little spout. There are also transitional formulas that are not as thick as baby formula but are heavier than plain whole milk and contain more nutrients.