bear in mind that I'm not an Apple guy (haven't used a Mac since System 7)
but .mov (MooV) is Apple's own proprietary container format for mpeg 2 & 4, and is quite old
AFAIK, mov doesn't support mpeg4 part 10 (ie. mov does not support the newer AVC video codecs including H.264)

.mp4 is an international standard container for all mpeg4 formats, (including part 10) and is heavily based off of apple's mov file format

where you can, use mp4, as it's newer, is an ISO standard, and is properly supported cross-platform

you may be able to just change the extension, try it
but chances are there's an option somewhere in QT to make mp4 the default container