Yuck. Everything running on one machiine.
To ease your transition, I highly recommend planning on setting up a new Public Secondary DNS server at least a week ahead of time, register it and leave it running during the entire time of your tranition (at least a week after you actually move). This is because mailservers typically cache mail domains longer than the configured Public DNS TTL you configure.
Moving a mailserver can be complicated, be sure to review your method of anti-spam, some are based on domain name only, some are based on IP address.
I would even consider planning on possibly running duplicate mailservers in both locations (depends on the capabilities of your type of mailserver to support a farm), then consolidating the mail stores later.
Although mailserver transition can be tough and Public DNS can be tricky, review your other services also. Private DNS can actually be braindead simple because it can literally be forklifted to the new location without modification.
HTH,
Tony