Interesting answers. I agree that the best course of action is to ask your doctor about your particular child.
Generally, though, having your child take a mutli-vitamin is a safe practice, perhaps with some benefits. Research shows that it is better to ingest our vitamins as part of natural foods and dietary habits, when possible. But the use of vitamins in children addresses the natural variations and holes in a child's diet. In this area many people are deficient in Vitamin D, for exmaple. Children who eat mostly bread and cheese can be deficient in vitamin C and iron. A simple multivitamin can help fill in the gaps. Children's multi-vitamins, including those with iron, won't even approach toxicity if the child takes an entire bottle in one day. A daily dose, even over a life time, will not approach toxicity in a healthy child. (We don't necessarily eliminate excess as waste, but we do use the vitamins up.)