If you're still concerned about whether or not you can get married, then I'd say yes. This is assuming that you and your girlfriend have both never been married or if you have documentation to prove you are now divorced from a prior marriage. Above, you said you were in Ontario. I'm an American who married a Canadian in Ontario in January. All that's necessary is to go to city hall and fill out the required forms. I believe there is also an online application which is still probably available at city hall however already filling it out beforehand makes everything faster. Both of you will need TWO forms of identification, one of which must have a photo (I used an American driver's license and my passport).
The rest may be specific to Toronto, but we received the marriage license right then, after 10-15 minutes, along with another form which you'll need the person who conducts your marriage service to sign (along with two witnesses). You can also have the marriage service in Toronto City Hall after establishing a day/time and paying the fee. Most people don't do that though, I think. If not, you'll need to find your own person to do the service, religious or civil. You'll need them to fill out the form which verifies they have in fact married you. They will send that form to the Ontario registration office and at the same time give you a Record of Marriage. This will be your official document of marriage until you can get the Marriage Certificate (it's better to have the MC to send to CIC, I've heard).
In order to get the Marriage Certificate you need to wait about 6-8 weeks and then apply for it (online or by paper). You'll receive it probably 2-3 weeks after that. The MC will NOT be sent to you unless you apply for it. And you cannot apply for it immediately because the request will be denied until the Ontario registration office has registered the marriage, which is why you need to wait 6-8 weeks.
It's actually very easy to get married (at least in Ontario), I had no problems as an American citizen. The marriage people aren't there to judge whether it's a marriage of convenience, love marriage or even forced marriage. They only care that you meet the requirements for it.