I think there is a difference between babysitting someone else's child and babysitting a sibling. A child is allowed to be left at home on their own at the age of 14, and I think at this age they should be responsible enough to babysit a younger brother or sister.
I think when it comes to babysitting a child of a family, then it should not be until they are 15 or 16. For babysitting as a part time job, where they may not know the child they are looking after, I don't think they should be babysitting at all unless they have been trained.