I am really confused, here.
When I go to 'Help' -> 'About QCAD', it shows the following (exact quote):
Version: 22.214.171.124-Free-1 [Community Edition]
Date: Nov 21 2010
(c) 2001-2005 by RibbonSoft.
(c) 2009 Jani Frilander
Yet, it autosaves, and I have looked high and low (including going to 'Edit' -> 'Application Preferences', and 'Edit' -> 'Drawing Preferences') and I cannot find anything to do with auto-saving.
Not knowing any better, I can only assume that my version of QCAD has been compiled from source with the autosaving feature built in but without any way for the end user to alter it. I am running QCAD under Ubuntu 11.04 (Linux) and got it from the included official software repositories.