Hi Daniel,
I would say yes, you can move your Qt application to a BeagleBone. You’ll need a DVI cape to have a screen but after that I think you’re good to go with Ubuntu or Debian. I found Debian more minimalistic but still quite enough on this board.
Cheers,
Bence
2012/9/25 Ichthyophagy <ichthyophagy@gmail.com>