The timing of this is interesting. I just created a work item to create an article with instructions on how to do this. It will be available sometime this month, but some rough directions are as follows:

1. In the RTC client, disable outgoing sync.
2. Shutdown the CQ Connector gateway.
3. Make sure CQ is installed on the new machine.
4. Make sure the CQ schema repository name and user db must remain the same on the new machine.
5. Install the CQ gateway on the new machine.
6. Copy over any user-configurable files that have been modified to the new CQ gateway such as the cqconnector.properties file and tomcat files (server.xml, tomcat-users.xml, web.xml)
7.Change the url of the external repository connection to point to new CQ gateway.
8. Start the new CQ gateway.
9. Enable outgoing sync.