Yes, alas that was the second time we failed to incorporate Canada.
However, strategically, the War of 1812 was a success. Naval defeat on the Great Lakes ended British influence in the upper Midwest and the Ohio valley. The Battle of New Orleans, though technically after the war, put an entirely different spin on the Treaty of Ghent, effectively ending both Great Britain's imperial aspirations and remaining influence with native Americans in the Mississippi River Valley. US Naval frigate actions defeating British opponents in ship to ship actions ushered in two centuries of growing American Naval power. Though ignored by the Treaty of Ghent, impressment ended with the end of the war.
I have great respect for what Canadian forces contributed in both World Wars and the Cold War. The best armored brigade in NATO was Canadian through the 1970's. It is what makes me so sad about the appalling condition of the Canadian armed forces today. Canada is totally dependent upon the United States for logistical support to what remains of its Air Force and Navy, and the remnants of its ground forces are essentially non-deployable by national means. Nearly half of Canada's front line military aircraft or non-mission capable. The navy has no replenishment ships to support what remains of the navy should it wish to unilaterally deploy.
I suppose it doesn't matter to most Canadians that they are unable to protect their own national interests beyond their borders, but I am not sure what that says about the reality of a nation's independence.