how do I get a Quicktime video window to play on an external monitor, simultaneously using the laptop for something else?
In Quicktime Player, go to Preferences. Under "Full Screen", there is a picture of your screens similar to the Displays pane of System Preferences. If you click on a screen, a picture of the QT Player logo will be overlaid on that screen. The screen that has the logo is the active screen for Full Screen Mode.

EDIT: I don't know if you can still do other things while QT Player is full screen.