It could be done (with a mountain of AppleScript).
Since you don't know the frame location wouldn't you need to have the QT file open to make your selection? You couldn't just set a time, say 00:00:30, and capture. What if that frame was out of focus or out of context to your goal?
The free AppleScripts from this collection could get you started:
http://www.apple.com/applescript/quicktime/
Even the free version of QuickTime Player allows you to copy a frame. Just position the playhead on the frame (use the arrow keys to step through frames) and Command-C. Bingo. An image on your clipboard ready for pasting into any image editing app. Or even use as a custom icon on the original QT file. Makes finding the correct movie from a folder of dozens very easy.
The Pro upgrade allows "Export as Picture". An AppleScript (from the collection above) can save the frame in .bmp, .jpg or .pct formats.
Another tip above images from movies. If you resize the QT Player your image file will be in this new dimension (a 320X240 movie resized to double will make a 640X480 image).