Can I control QuickTime Player with the keyboard?
Yes, there are certainly ways of achieving this result on QuickTime Player. Here are two ways:  


You can use the spacebar to play/pause the video as long as your
active (front) window is QuickTime Player and not another software, 
perhaps the one that you use to transcribe.
If you use the left and right arrow keys, you can jump backward and forwards a frame - keep it pressed to speed things up. When used in combination with the Command Key, you can achieve x2 speed rewind/forward, then hit the spacebar to stop at the desired point in the video.  


I have to admit that this method requires a little bit of fast keyboard action (compared to other apps) but that is something one can get used to. There is a full list of shortcuts that you can look at in case there is anything else you might find useful. Perhaps slowing the video down is an option.
Anyway, let me know how you make out.