So Canadian nationalism really had its genesis during the war of 1812. What would have happened if it was avoided, would it have pulled a Texas latter or What?
It seems unlikely that the absence of a War of 1812 would have greatly affected the trajectory of Canadian history. The rebellions of 1837, the Union Act of 1840, and the 1867 Constitution Act were the foundational events for Canada, not the War of 1812. The implications for the US would have been greater. If the War of 1812 had been avoided, the Andrew Jackson would have been denied his epic moment at New Orleans and probably his Presidency. Without his expansionist aims, and those of his proteges (Polk), the geography of the US could have turned out quite differently. I explore this "what if" in the last chapter of Neither Victor Nor Vanquished.
Canada would probably not be very different. It's possible that there would be less fear of the US, which could lead to better American-Canadian and American-England relations earlier than OTL.
In the US, on the other hand, the butterfly effect would be huge. The War of 1812 played a major role in cementing racial consciousness in the US (this was when the Army was first segregated), as well as a hatred of Native Americans (who sided with the Brits IOTL). The Federalist Party would likely survive a little longer. The failure of the militia system wouldn't be obvious, and the US might take decades to get a real standing army, which has bad implications for Manifest Destiny (possibly a bloodier Mexican-American War, with the US getting far less territory than it did IOTL). Andrew Jackson wouldn't have become all that popular, which means the US Central Bank might survive.