How can I move my Windows DNS from one server to another with minimum disruption?
Both servers are in the same domain and we do use DHCP for the windows clients but the servers are fixed IP.
DNS is Active Directory intergrated.
It sounds like you have two problems. Moving the DNS zones to a new server and directing clients to the new server.
Moving the Zones
Assuming the DNS zones are Active Directory-integrated this is just a matter of promoting the new DNS servers to being domain controller computers, as only domain controller computers can run DNS servers hosting AD integrated zones (http://technet.microsoft.com/en-us/library/cc978010.aspx).
If you're not using Active Directory integrated zones (i.e. standard zones), you can use a script that I wrote in this answer to migrate the zones from one server to another: http://serverfault.com/questions/37960/migrate-200-domains-from-win2003-dns-server-to-another/37976#37976
Directing the Clients to the New DNS Servers
Windows clients that are statically configured to use the existing DNS servers will require changes to be made, either manually or by using an automated tool such as "netsh". If you've got a lot of statically-configured machines using a script would probably be easiest.
Clients that are receiving their DNS server assignments from DHCP are much easier. Change the DNS servers specified in the DHCP scope and wait for the lease expiration time before decommissioning the old DNS servers.
Finally, if you've got other operating systems (embedded devices, etc) that have the DNS servers specified be sure that you change them, too.
Ideally, you should attempt to dedicate some IP addresses for your DNS servers such that those IPs can be re-assigned to other server computers in the future, rather than having to go through this ordeal ever again. Try and refer to all servers / services by DNS name, in the future, and keep the IP addresses used by the DNS servers free to be re-assigned to new servers in the future. (Don't, for example, also use the DNS server IP addresses as the address specified for some other kind of service program that might not always reside on the same machine as the DNS server software. If necessary, assign secondary IP addresses to the DNS server computers for such purposes.)
One other way I use to copy a zone is to setup a secondary server that zone transfers the zone, then change it to primary.