First things first: Decide the course that you want to take.
You can either decided to apply for PR through being common-law partners, or through being spouses.
If you choose common-law, you will have to be living together for a year and sharing bills, leases, bank accounts, etc. in order to prove your relationship to the CIC. You will also have to apply for a Vistor's Visa Extension. If you are from the USA, this will not be a problem. Especially if you explain that you are pregnant. After a year of living in Canada, you can apply for PR through sponsorship and wait. You will not have any health insurance and your will be unable to work until you get PR.
If you choose marriage (which is what I suggest) you would found out the process of getting married in the Province you live in (I know about Quebec/Montreal if you have questions), gather all of the proof you can of your relationship (the pregnancy will give you a lot of points.
) and send in the application for sponsorship and PR. Once again, you will not have healthcare until PR is approved but applying for spousal sponsorship is going to be much faster.
Cilioca is right though, you need to make sure that you have healthcare coverage in the province that you're in. Applying as Common-law partners typically takes more time and is much harder to prove than if you were to do it as spouses, but if you're not necessarily ready to marry each other I do not suggest it. Your sponsor will be responsible for you for 3 years after PR is approved, and it can cause a lot of problems if you do not stay together.
