You can export Test Cases with their associated Test Plans in RQM by "Browsing" Test Cases and switching View As- - "General" to "Traceability View" and adding the "Test Plan" under "Change Column Display Settings".  This however doesn't also allow the associated Test Script(s) to be displayed / exported.

What is the purpose of exporting test artifacts? Is it for reused in other environments? RQM does not provide export and import feature for artifacts so that it can be portable. If you want to have a "copy" of the same artifacts from one project area, you have two ways to do:

1) if the source and target project areas are in the same server, you can use artifact's "duplicate" feature(on the right head menu)
2) if the servers are different, try copyutility:
https://jazz.net/wiki/bin/view/Main/RQMCopyUtility
(using this utility, you can copy to the same project area or other project area in the same server as well but the built-in feature in 1)'s scenario would be easier in most cases)

CopyUtility can be found from the jazz.net download page, for example, v4.0.5 is in:
https://jazz.net/downloads/rational-quality-manager/releases/4.0.5?p=allDownloads

Hopefully this helps.