First off, to qualify for common-law, you need to live together 1 year, not 3. If that helps.
But anyway, I don't know anything about the way your fiance is going to Canada. Will she be becoming a permanent resident or is she only getting a temporary work visa? If she won't be a permanent resident (and from what I've read, she will not), then you don't really fit in family class. You need a permanent resident to sponsor you. Maybe you will have more luck asking your question in the Skilled Worker / Professional Immigration forum, people might know more about this there.
Or just wait for PMM here, he seems to know everything
