Quickly Move DNS.
The answer is you can’t but don’t back button yet, it only takes a few steps. Let me explain.
Some DNS stuff is inherent and other stuff is referenced. For that reason it can’t be discovered 3rd party. Things like A, MX and TXT records are inherent while sub-domains are referenced.
Inherent records (my name for it) can be looked up using things like MXToolbox.com. Or dig a Nix command that exists on most distros. My favorite UltraTools DNS Lookup Tool , it does the best job of interrogating inherent DNS information and dumping it compactly.
Referenced DNS on the other hand is a manual process. You’ll have to log in to the host and document them.
I’ve heard rumor that you can export DNS, to my knowledge there is no standard DNS format and therefore no reliable way to export and import DNS.
If you have a better way let me know.