Apparently there's no native method to automatically close Quick Fields upon session completion.  But for those looking for an answer, I figured out how to accomplish this, plus kicking off a session on a timetable to run automatically like Import Agent.  Look at Macro Express Pro ($69).  Create a fully automated macro that closes down QF when it ends processing by looking at the change of color of the text in the output pane.  Note that the standard text black is followed by blue to show the end of session report.  You can pick up this color change, whenever it happens (check every 2 seconds), and then issue the macro keystroke commands to close out the session.