And interesting account of the War of 1812 can be found on YouTube. It's a Canadian produced documentory about the conflict starting from the American Revolution to the end of the War of 1812. This is a link to the first part:
http://www.youtube.com/watch?v=Zl0SUidXnuA
I learnt quite a bit from that, which surprised me somewhat. Normally all I see in regards to the War of 1812 on YouTube is American stuff that focuses on Impressment, sometimes the arming of the Indian tribes, then brief mentions of the burning of York, a whole deal on the burning of Washington, a few naval skirmishes and then a jump to the Battle of New Orleans. I learn more about the war from that series of clips than I had learnt from watching dozens of American stuff about the war.
Anyway, in the third part it talks about the Canadiens' being loyal to the British, being revolted by the French Revolution, fearing American subjugation of their culture and way of life and their determination to defend their home from American invasion. So with the Canadiens' being content with life under British rule and fearing what domination of their way of life would come under American rule I dont think there was ever a chance of Quebec joining the US.
Other comments in other threads I've seen tend to back you up on this, which is why I was keeping the option of an independent Quebec open. The US, if it is militarily victorious in the north, would want some way to parley its success into a permanent advantage. One would be to seize Canadian territory--which will evidently be fraught with the danger of ongoing discontent. If the Americans are wise enough to see that, then one fallback is to negotiate a status for Quebec that weakens the British position in the north.
If they liked the Bourbons so much, perhaps an arrangement can be reached where the dynasty gets parked in Montreal pending an eventual restoration in France; then Quebec by treaty remains a French duchy with a cadet line remaining in Montreal as Duc while the senior heir returns to Paris. By treaty, Quebec itself is largely demilitarized and so are British holdings to the West; reciprocally the USA agrees to low levels of military preparation from the Quebec border westward as both British and US presence moves that way.
Events in Europe would therefore have continual disturbing effects in North America; every time the French regime changes, the status of Quebec gets thrown into question. Presumably when Charles X takes the French throne someone closely related to him becomes Duke of Montreal; then assuming the revolution of 1830 happens as OTL and the house of Orleans takes the French throne, Quebec's ties to France get severed as the senior Bourbon surviving arrives to be the French Pretender in exile--well, perhaps he doesn't take refuge in America after all. OTL the rise of the House of Orleans in 1830 was the end of all Bourbon French monarchies though later generations of royalists held on to hope of a Bourbon restoration; with the house having a refuge in Canada these might be more of a real possibility.
It could be that meanwhile, the Quebecois change their minds about supporting the Bourbons, depending on how the house conducts itself in Canada. Meanwhile too, the relation between Britain and the USA is also shifting; Quebec's independence depends on the treaty, imposed by Yankees in 1812, holding. It could be that Americans will think they have a better chance later at taking Canada and violate it, or that the Quebecois denounce it and rejoin the British system, tossing out the Bourbons (and triggering another round of war with the Americans--or perhaps the Yankees are astute enough not to go to war if the outcome doesn't seem too immediately threatening).
With the treaty holding and France evolving much as OTL, the eventual early 21st century outcome might be that Quebec remains an independent Duchy, perhaps renaming itself a Kingdom eventually as all hope of a Bourbon restoration in France is lost. To be compatible with its British and American neighbors the country will have evolved into a constitutional duchy/monarchy. Canada forms as a British Dominion around it.
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Alternatively, another possible Yankee solution would be to take only limited territory from their 1812 conquests, say a salient of Quebec to give the USA a strategic frontage on the Saint Lawrence. That way the Americans threaten to cut off the river in case there is some subsequent major confrontation between Britain and the US. But otherwise, the British dominions are left free to develop as they choose.
One possible outcome of that would be a major backfire of the intent compared to OTL. OTL, eventually the US/British border was gradually demilitarized. But with Americans choosing to rely on a threat to protect their interests westward, the British might seek to counter it with as much force as they can muster, leading to the ongoing militarization of the long US/Canada frontier. Perhaps that border would not be mostly a simple latitude, but would be frequently contested thus adjusted into a complex curve reflecting the local geography and the outcomes of a series of armed struggles.
If that happens, I'd look to a lot more British intervention in every American crisis, notably any possible Civil Wars; vice versa Americans (if not shattered by such divide-and-rule maneuvers) will take advantage of every moment of distraction and weakness that Britain suffers. It could be that come the early 20th century and a possible great power showdown filling in for OTL WWI, the Americans will automatically take whichever side opposes Britain!