My baby is one year old. Sue Gilbert Sue is a consulting nutritionist. For many years she worked with Earth's Best Organic Baby Food, integrating nutrition and product development. She has written numerous articles on children's health and nutrition for parenting publications. What is important for your 12 month old is to eat a diet with a wide variety of food to get the appropriate balance of nutrients that he needs.
Eggs are a wonderful source of protein, vitamins and fat.
If you are choosing eggs as his source of protein because he likes them, and he isn't eating meats, cheese, or other protein foods, then by all means, allow him to get his protein from eggs. One egg a day is not too much. Your little guy should not eat so many eggs that he is not hungry for other foods that he also needs to eat. If he is also getting egg in other foods, such as puddings or baked goods in addition to that egg, it is fine. Those eggs are coming with a variety of ingredients that are contributing to the diversity of nutrients in his diet.