If you are truly a female student wanting to stay in Canada, you have good options to stay by yourself:
1. After undergraduate study (in Ontario for instance), you can work for three years. This means you can apply for immigration during the period.
2. If you have a Master's degree or above, you will be granted permanent resident status by Ontario if you apply.
Check out immigration policy related website by yourself.
Common-law normally doesn't qualify for spousal immigration. Even if you are married, there is no guarantee immigration will be granted. Plus, it may take a few years. If there is any change in martial status, the immigration will be in jeopardy.
If you are serious, then be serious and don't "sell" yourself. It is a trap...