This is neatly ignoring the role which British favour for the Québécois was a major cause of the American Revolution; things would have been changed very much if the British had taken the anti-Québécois position that the British colonists in North America preferred them to take. To imagine the Québécois siding with the fiercely anti-Québécois American revolutionaries is utterly beyond belief, unless we go for PoDs sufficiently long ago as to butterfly the American Revolution, and thus the USA (if it even has that name), beyond all recognition—though I do think, for various reasons, that some sort of conflict vaguely along the lines of the American Revolution would probably still happen sometime. The War of 1812…? Forget it. Positing changes to the prelude to the American Revolution and asking how the War of 1812 would have gone is like saying "If William of Orange had never invaded England, how would the Seven Years' War have gone?"
As for Quebec, there's a rather larger problem. The American Revolution would not have succeeded without French support, and the French made very few gains in the conflict, although they did much of the fighting and bore a huge amount of the expense (France essentially funded and armed the American war effort). As it turned out IOTL, France lacked compensation. You're proposing that a sizeable number of Francophones be liberated from British rule, and France gets nothing, and the USA (which owes its triumph to France) gets a Quebec which is under its own republican ideology, and France is totally alright with this resolution.
Surely not! The obvious outcome of Quebec rebelling against the British isn't a Québec libre, it's a Québec française. And if we pose a resurrection of French North America, we're going to get butterflies the size of pterodactyls. It's in doubt whether we see a French Revolution, let alone a War of 1812.