(to clarify: DNS+domain at the same service can be OK, as long as you have nothing else there. As soon as you start having other stuff, keep the DNS there, but move the domain registration away. Depending on which domain make sure you have auth keys, access to the admin domain or whatever would enable moving the domain without registrar cooperation. In my hosting days I did my fair share of emergency transfers and infrastructure to help companies get their basics online again after a SNAFU - totally doable to have first mail coming in again within a working day)