Most states do not have any formal laws surrounding how old a child should be before they start babysitting. The state of Michigan recommends that a child be 12 years old, but the decision is ultimately left up to both the babysitter's parents and the children's parents.
Caring for children is a big responsibility. All babysitters, regardless of age, should be mature and responsible. I recommend encouraging your child to start gaining experience by caring for children while an adult is present. Once your child has gained some supervised experience and has proven that they are responsible when caring for children, they will likely be ready to take Babysitting 101 and start babysitting independently.