transfering DNS from server to server

Hi there,
How can a transfer zones from one DNS to another, making the second one as Default DNS server and uninstalling the DNS role in the first one.
The DNS is installed in the computer that is a default gateway with 2 NICs (external IP, and internal one), and acts as web server. The second computer is part of the domain and will be the default DNS server.
My concern is if the the DNS server should be the default gateway or any server in the system and do I have to get install the IIS in this computer.
Both computers have 2003 running and are part of the same domain.
Thank you