Is a healthy diet particularly important at any particular age of childhood?

All ages. Living a healthy lifestyle (including a healthy diet and being active) is important at all stages of life, from infancy to adulthood. It is especially important for parents to role model a healthy lifestyle to young children, as they are very impressionable and the habits they form early on will stick with them as they grow older.
Yes YOUR child's age. Experts would argue that a healthy diet is important from the very age of conception--encouraging the mother-to-be to choose her diet wisely. Others suggest that the immensely rapid brain and eye development during the first few months after birth are vastly influenced by early dietary selections. Yet, we can only control the diets of our children now--in the present. So now is the most important.
Definition may vary. Dr webb is right, building a healthy life requires good nutrition at all ages. Your definition may vary some in the turmoil of toddlerhood.Attitude & a reduced daily calorie need will drive many crazy. I find these kids eat well 4-5 days a month and graze the rest.No one wins a food fight, so get used to a balenced week rather than a balanced day until older.Only offer healthy food reguardless.