Quebec actually has a different legal system altogether. It is not based on English common law as Canada. Per nation quota at federal level will face legal challenges due to its conflict with charter.
I remember Quebec restricting hijab, turbans etc in public employment. The reason why it worked was because Quebec has a different legal system and invoked notwithstanding clause in Canadian charter. Federal government till date has never invoked that clause ever since 1982. And yes Canada had a lot of spats on immigration in past as well.
For Canadian federal government to implement a per nation quota, they will have to invoke Section 33 of the Canadian Charter ie notwithstanding clause. It will be unprecedented in Canadian legal history and bigger issues will be at risk then and political fallout involved in it. Not to mention it is temporary in nature and will be required to be reinvoked again and again after every 5 years.
https://www.justice.gc.ca/eng/csj-sjc/rfc-dlc/ccrf-ccdl/check/art33.html
Notwithstanding clause in Charter is a rather sensitive topic in Canadian politics. Its very similar to "more equal" in animal farm. I doubt any coming government will stir that pot.
Once a precedent is set, it is a slippery slope from there on with racial and gender discrimination at the other extreme.