Currently there is no built in functionality that will allows a user to move a Project Area across  servers; the two alternatives, but each have their limitations.

1) The RQM copy utility
The Utility was never meant to be used as a 'Project Copy', but rather as a means to re-use specific test assets. It is however capable of performing a Deep Copy; this is not a full copy Project Area, but the majority of the Project Area assets are copied
I would fully review the Known Limitations sections of the Wiki (https://jazz.net/wiki/bin/view/Main/RQMCopyUtility#Known_Limitations) so that you have a full understanding on what and what does not get copied


2) Server Rename
The Server Rename functionality allows you to copy the entire CLM set up from an existing environment to a new one
A couple of things to consider:
    a) You cannot pick and choose which Project Areas to copy; everything is copied by default
    b) You cannot perform the rename to an existing server (meaning you cant merge data from server A to Server B; server B will be a copy of server A)
If you are interested in Server Rename, there are a few articles on Jazz.net that can be reviewed