Does your doctor have to see your 1 year old when he is ill?

Usually, yes.

Very few doctors will be happy assessing an ill child, especially one as young as a 1-year-old, over the phone. If you are worried enough about your child's illness to call a doctor, then they will ask you a series of questions about their condition, and if they are happy that your child is quite well, they may give you advice over the phone. However, if they are concerned, they will ask you to bring the child in to see them.