I'd just back up the zone files. Look in system32\dns.
If it's "Active-Directory Integrated", then first change it to "Standard Primary". The zone file name will be shown on the properties page.
Never tried it myself, but on the new server you should be able to just set up the zone as Standard Primary with the same file name, stop the service, copy the old zone file, and restart the service. I'm not sure you need to stop/start the service, but it's normally needed.