yes you can give them eggs
to boost the immunity you just have to give a proper diet which consists of 1) 4-5 meals per day
2) variety in meal like oats, daliya, mashed fruits, cerelac, curd rice, boiled vegetables etc etc
3) add a tsf of ghee/ butter to their prodigy
4) add lemon juice few drops, tomato pieces, to their dishes you cook
Next Steps
hopefully these will help you