Psychiatric drugs should be prescribed for children in extreme cases. Just think what would have happened if kids and young adults who turn violent with school shootings had gotten psychiatric help before they went nuts and killed a bunch of people? I think psych meds for children should be a last resort, but if helps them to lead a normal life, then go for it.
Yes, doctors should prescribe psychiatric drugs to children, because youth is often the best time to treat mental issues. If a child is treated, it can prevent a small problem from becoming a large problem in later years. If the child absolutely needs the treatment and stands to benefit from it, there is no reason that the child should not receive the same help that an adult would receive.