Doctor What said:
England will never allow 'their' colonies (or newly independent nations) to stray too far from the motherland--they'll be keeping a close eye on their assets, especially after the RW and these noisy 'americans' down south. Quebec was always seen as a bit of a pain in the ass from day one--if it was granted independence, I suspect they'll take steps to make sure that the new nation also stayed in line.
In 1869, when Canada was formed, Lower Canada (Modern Quebec and Labrador) already had had responsible government for 30 years, which meant they controlled their internal policies. Its plenty for the tastes of most Quebecers, and without the new authority coming from Ottawa, most would have had no problems with nominal english sovereignty up to modern days. Most likely by then Quebec would have gotten a Westminster-equivalent status, and in modern times, they could obviously throw away the Queen at their leisure if they felt the need.
Also, Quebec's nationalism was mainly felt in the first half-century of the conquest and in recent times. Between 1763-1840, they had too little rights as a nation to accept what the English tried to impose on a regular basis. Since 1960, Quebec has become a modern nation, with a politically conscious population, which has a hard time accepting not to control its own destiny, so of course, a surge of nationalism was inevitable.
Since the former period is pre-pod, and the latter so late that the British cannot enforce anything anymore, the POD proposed is unlikely to cause conflicts between Quebec and London.
What was said before remains though; for these reasons, an attempt at forming a confederation would have been almost unavoidable. Perhaps very strong resistance against federation in several parts of Canada might have tipped the scales though. Some regions, like Newfoundland, had no interest in it from the ground up.
World-scale impacts of the POD would be minimal.
Some friction with England during the Boer war. Less Lower-Canadian troops in Europe in both world wars, of course, since a local government would have never imposed conscription, opposed by upwards of 85% in both wars. Quebec's science and technology would have more of a chance to develop, without OTL's interventions by Ottawa which were generally hugely detrimental.
For exemple, in the early 1960, Quebec's fledging aeronautical industry developped the best air-superiority fighter in the world, far outclassing any other jets in existance at the time. Though all NATO nations wanted to purshase them, Ottawa sabotaged the whole affair for (english) economic and political reasons, and Quebec ended up selling only parts for years, until the technology was obsolete.