I will tell you what I know from reading at CIC and from various forums, but I am not an expert. If you want to be a student in Toronto, you would be considered an international student and I think you might need a student visa. Not really sure. It would also be quite expensive as you are not from that country.
You would have to look into a student visa if you wanted to take this route. There are categories on this forum that you could look at to find more information.
Otherwise, you don't qualify for permanent residence. I'm in a somewhat similar situation. My husband is Canadian and I'm American. The best option for us to be able to be together was for us to get married first so that he could sponsor me as his spouse. You don't qualify as common law unless you are living together for a year. Conjugal only works if you can prove that there is a reason that you couldn't live together for a year, and a job does not count as a reason. So, we got married. We're in the process of applying for permanent residence for myself, which if you apply outside Canada takes anywhere from 3 to 12 months depending on many things.
Start reading at the CIC website and you can weigh your options.