You don’t copy Active Directory from the old server to the new server. You add the new server as a domain controller within your existing Active Directory domain by running dcpromo on the new machine and going through the wizard. Once it is done both machines will be domain controllers with a full copy of AD on it.
If you need to remove the old server after that you have to move all the FIZMO roles to the other server, then run dcpromo on the old server to tell AD that it isn’t a domain controller any more.
If you only have one domain controller now, it would be recommended to leave that server online so that you have two domain controllers in case one fails.
Check out this thread as well: http://social.technet.microsoft.com/Forums/en-US/winserverMigration/thread/867740f0-3ce3-406d-9667-efd392da75b3