Bring up the Server 2003 system and load DNS.  Configure a new zone,
type secondary.  Point to the same zone in the NT system as the
pirmary.  Let the zones replicate (or reload/transfer from master).
Change the Server 2003 zone from secondary to primary.  Take the NT
server offline.

Naturally, you need to change the DNS records on clients and in your
registrar's settings for your domain if it's registered, or you can
add the IP address of the NT system to the Server 2003 system once the
NT system is offline.  Permissions for zone transfers is about the
only thing you can mess up here, and that's simply adding the opposite
system as one allowed to transfer to/from.

Jeff