Until a child starts eating solid foods, breast milk is the best diet. Even after starting solid foods breast milk should be slowly phased out. Children of any age, after getting off breast milk, should eat the same balanced meals that an adult vegan would eat.
There have been stories of adults feeding their children a horrible vegan diet like the celery only diet. That is a very dangerous diet especially for children. Their brains are developing very fast and they need proper nutrition. A good vegan diet is such a diet. The mentors on this site are more than happy to answer any of your questions. Just ask!