Hi FK, it all depends how you want to do it. If you join the Tagesmutterverein (Child carers association) in your local commune they take care of all your contracts, AHV etc.
If you remain independent then you'll have to take care of your own insurance and pay the whole AHV portion yourself but still register as a child carer. I don't think this would be too complicated and you'll find all the information you need at your local commune or family center.
If you need help with German translation feel free to get in touch.