Or have a child together. But common-law relationships and marriages are not the same thing in Canada, whereas other places where common-law marriages are recognized, they are legally identical to other marriages.

That's a bit misleading. The specifics vary by province. eg. Common Law kicks in after 3 years living together (in a marriage-like relationship) in Ontario, and after 2 years in BC.

Revenue Canada has their own definition of common law, for tax purposes only (not litigation), which is independant of that and is 12 months.