I don't think it's possible--to copy you would probably have to go through the XML files in the QVPR and manually copy the entries. Depending on the type of task you want to copy, there may be several relevant XML files. Note that this will also require a restart of the Publisher server after you're done copying. It's probably just easier to create a new task :)
QVS 9 SR6 now has a Copy Task capability. Click on any source document that has a Task. In the right panel you will find a Copy Icon to the left of the Start Arrow in each Task associated with the document. After clicking the Copy Icon, you can then use the Paste Icon to the left of the + sign (Add Task) in the upper right corner of the right panel.
Copied Tasks can be Pasted to any source document and then edited to fit that document.