If you have agreed price / times / etc... you have a contract. A minor cannot be liable and cannot be held to a written or verbal contract so the dog owner is liable for anything that happens, from the dog escaping and causing an accident, to a claim for cleaning bills because the dog jumped up to be friendly. So anyone giving a dog to a minor is taking a huge leap of faith that nothing will ever go wrong. Not a risk I`d take. This is why jobs for minors (working in stables, shops etc) should be supervised ones.