The Q: drive is created when a Click to Run version of Office is installed.
The most common ways of getting CTR Office is as part of the free "Office 2010 Starter" or via an online download purchase of Office.
If you are using a CTR version of Office, leave the Q: drive alone.
Otherwise, are you having some sort of problem with the Q:\drive? The only way to "get rid" of the Q:\ drive is to Uninstall the Office CTR that is using them. If you do manage to hack into Q: and get rid of it, the associated Office CTR will be broken.
Am I running Click-To-Run?
The quickest way to verify you have a CTR installation is go into Windows Explorer and look for an unexplained Q:\ (or R:\) drive.
Another method of checking: Go to help panel of any working app: File tab / Help command and look at the Right side of the Backstage panel. It should say "Product Activated" for MSI install or "Click-to-Run Product Updates".
If you installed Office 2010 using Click to Run technology, there are no Office files on the C drive, but on a virtual Q drive. "Microsoft Office Client Virtualization Handler" will appear in the list of programs. Associate the Office files with that