Originally Posted by Auld Yin
You can apply for a TWP from within Canada provided your employer is willing to go for a LMO for you. If not there's a good chance you can extend your visa but make sure you do it in a timely fashion. If your girlfriend gets a job she can also ask the employer to apply for a LMO and can possibly get her non-student visa extended. Very often such decisions are at the whim of the CIC.
Do you live with your girlfriend in a common-law partnership? I guess you can register as partners once you move to Canada on BUNAC. Common - law partners who have lived together for more than a year, have same rights as spouses which means that she will receive visa once your work permit sponsored by your employer will be approved. That's what I understand but it is worth to consult CIC web page, anyway.