I will assume by leaving you mean not intending to come back; although it is not ethical, yet you can do that.
Also you will have to consider that all GCC countries are linked through a police system; i.e. if you left Qatar and headed to Dubai, you could get arrested there and resent to Qatar for prison.
From what I heard, few Arab countries (I know it is one country so far) have signed an agreement with Qatar, by which you could also be pursued in the such country (other than GCC)