You only need to apply for an ARC if you have entered the country on anything except one of the visa-on-arrival provisions. Whether you know it or not, you entered the country on a B-1 visa (사증면제) that was granted to you upon arrival for being a citizen of another country. The overwhelming majority of B-1 visas will be for 90 days, but for Canadians it is 180 days.
If you have arrived that way, I don't even think that you can apply for an ARC.
If you're really anxious about it, the best thing to do is to talk to an immigration lawyer. Depending on where you are, there will be lots near the immigration offices (출입국관리사무소). Canadians get all sorts of special treatment, though.
Unless an immigration official or consular officer stapled one of these in your passport:
I wouldn't worry too much about having to apply for an ARC.
Edit: Actually, even the official website indicates that "foreigner stay" is categorized as either short term (less than 90 days) or long term (greater than 90 days) stay, and that long term stay requires that you either register as a foreigner or file a Domestic Residency Report within 90 days of arrival.
Your best bet will be to call the Seoul Global Center (02-2075-4130, 02-2075-4131) and ask there. Even if you are not residing in Seoul, they can answer your questions.