Ninja, I've only registered full whitetail carcasses in the past. The only time I had to register a quartered animal was for moose.
I could look online and give you the official answer but it would do you no good. I suggest you follow the link provided above and do your own research. As a hunter, you are responsible for your own actions and cannot put the blame on someone online who gave you bad information when you are caught in the wrong.
That's my advice, from someone who hunted Quebec for 12+ years and who has heard all sorts of BS from "experienced" hunters. Normally, those are the same guys who'll shoot a Cow moose in a Calf and Bull only season... Do your own homework, check hunting seasons yourself and do not ask for any actual information on social media/forums that you can find yourself on official sites or hunting/angling extracts. Once again, I have seen many lazy people, in Quebec, Ontario and Saskatchewan, ask for regulations/rules on forums/facebook and get bad or wrong information. As a new hunter, you must seek and confirm all information on your own to make sure you are not in fact poaching. I remember sitting in my Hunter Safety course, 15 years ago and receiving bad information from the instructors, had I not read and understood the actual rules and regulations I would probably still be in the wrong and maybe have gotten caught and paid the price.
On the other hand, if you seek any advice or tips on hunting, this forum is one of the best place for information. I've hunted the Eastern Townships for 12 years and am more than willing to give tips or information.
Happy hunting and good luck!