As we know from watching "True Q", they were Q who decided to turn into humans and raise a child on Earth, and were eventually executed by the Q Continuum, being killed in Topeka , Kansas by a mysterious tornado that appeared out of nowhere despite weather control, destroyed their house, and vanished. And this reminds me of the opening of The E.E. Smith novel The Vortex Blaster (1960): http://www.gutenberg.org/files/22629/22629-h/22629-h.htm I don't know why "True Q" reminds me of this, but it does.
The idea of Q choosing to become human, being so abhorrent that they'd execute the 2 of them, always left me thinking about the ramifications of them turning Q into a human in Deja Q, knowing that he'd likely end up dead from that as well. How can you execute somebody for doing something "Forbidden" , then turn around and force somebody to do that very same thing, as a punishment, that'll likely cause their death too? It doesn't make any sense. I didn't like this episode mostly for that reason. The Q come off very inconsistent, or it at least retcon undermines their intentions in Deja Q, leaving you to think they really weren't planning on leaving him as a human, & letting somebody kill him