I think we should keep them separately.
One - Babysitter - should be questions about having a babysitter/finding a babysitter/interacting with a babysitter. (I.e., it's questions a parent would ask.)
Two - Babysitting, perhaps is better for this - should be for questions about the act of babysitting, for example about how to become a babysitter, how to be a good babysitter, how to approach certain things as a babysitter (such as discipline issues). (These are on-topic here, at least in my opinion, despite not being questions a parent would ask. If that's controversial I'm happy to discuss why separately.) These are questions a babysitter would ask.
These are totally different sets of questions, and so deserve different tags. Looking through babysitter, it looks like there are a few questions for the latter, and mostly for the former.