RQM have built in copy framework (Copy utility is external tool which leverages REST API ), using that you can duplicate artifact within same project area or copy to another project area on same RQM server.
e.g. Go to browse Test case
Select the rows which you want to copy
Click Duplicate action on toolbar. In case you don't see this option you don't have appropriate permission
A dialog pops up asking you the target project area
Select same or other project and click OK
There may be additional dialog to map category if target project is different and finally you click finish.
Done