Im also a vegetarian and I eat eggs every day. However, I also have other sources of protein. Soy, tofu, tempeh, beans, greens, tuna, cheese, hummus, milk, etc.
Just remember that each egg has 7 grams of fat. 3.5 grams in the yolk and 3.5 grams in the whites. So while eggs are good for you... they can add up in total fat.