That is what I am doing now, leaving Canada,If you entered Canada on a transit visa, then you are already out of status (in Canada illegally) and applying for a work permit from within Canada isn't possible. You would need to leave Canada and apply from your home country. The longer you remain here out of status the lower the chances the work permit is going to be approved once you leave and apply from your home country.
But what I want to know the process of work permit application for employer for LMIA exempted NOCs in Quebec