I am in a very similar situation except that I am in Ontario.
According to what I have read I need to live with her three years together to apply for the common in law status. We actually tried to do what Leon suggested. She extended the visa but then we realised that the law is different in Ontario.
We are both from different countries, so now she went back to hers and I am planning to visit her during summer.
We are planning to get married in her country. If we do that can we apply to common in law here in Canada? On the top of all of this getting married seems to be very expensive...
Immigration is not only in Ontario, it is federal. For tax purposes in Ontario, it may be 3 years, for immigration, it is still only 1 so if you live together for one year, you can prove it, you fill out your own declaration of common law relationship and then she applies for an open work permit based on your study permit, it should work.
If you get married, no matter in which country, you are also married in Canada so she could apply for an open work permit as your spouse.