No the war of 1812 is not and was not the largest war we have been involved in. With around 8% of the total population directly involved in one way or another with the war in Europe during World War 1 and roughly 3% of the population or 39% of the Expeditionary forces becoming casualties, I think that World War 1 ranks right up there, and that’s not even bringing up financial cost.
During World War 2, with 9.7% of the Canadian Population directly involved in operations overseas, and close to 1% of them coming back home with physical injuries or not coming back home at all I think it would be an understatement that it affected less people then the US civil war. After the fall of France, and with the fate of Britain hanging in the balance, it looked like Canada would be the next leader of the Allies. During WW2, tens of thousands of allied aircrews were trained during the war; Canada supported England with grain shipments, participated in the Battle of Atlantic, and arguably made the most important contribution in the Dieppe Raid in 1942. This war involved so much Canadian effort, and so much sacrifice that it is the largest and most effort consuming war Canada has been involved in.
During the American War of Independence, and the War of 1812 Canada/BNA was invaded, and out existence was directly threatened by the US, while during the American Civil war, although the threat was present, the US was not likely to invade Canada/BNA because England was THE superpower at that point in time.
And to add to your little issue with entanglements in the Middle East, Canada was on the terrorist hit list before we went to Afghanistan, remember when Canada was busy sending Canadian troops in poorly led missions following extremely stupid borderline criminal feel-good missions. The reason we have not been hit by a Terrorist attack like every other nation on the list, is because of the skill and vigilance of the Canadian security services and a lot of luck. Terrorist actions are unjustifiable, and I cannot begin to understand people who believe that we should pull out of Afghanistan and let them sort each other out. This are the people who poison teachers who educate young girls, have thrown acid in their faces, and yet we are accused of being the aggressors.