I agree with this statement: ( Just because Canada wasn't officially a country in 1812 doesn't mean this isn't Canadian history.)
As for the part that Colonial Militias where unimportant in the formation of Canada I would have a closer look at the Fur Trade.
During the War of 1812 William McGillivray of the North West Company volunteered its men, canoes and ships to George Prevost forming the Canadian Corps of Voyageurs.
The CCV had some spectacular victories two important men where Colonel William Mckay of Fort William (Thunder Bay, Ontario) and Colonel Robert Dickson of Dicksons Post (Minneapolis, Minnesota).
One of my ancent relations on my fathers side was Jean Baptiste Bisson he was an employee of the NWC and acted as a path finder and interpreter for Peter Pond, Alexander Mackenzie and David Thompson.
During Baptiste's time with David Thompson he helped him map the Columbia River and its tributaries his map was an invaluable resource to the Lewis and Clark Expedition.
Baptiste was with William McGillivray and the group of Voyageurs dispatched from Fort William to capture Fort Astoria (Portland, Oregon).
After the war he returned with David Thompson to help complete surveying and map making of Lower British Columbia and the states of Washington, Montana and Oregon.
David Thompsons maps where so accurate they have been in use up untill quite recently a testament to his skill a replica dons the Great Hall at Old Fort William Historical Park.
William McGillivray had been a buisness partner with Jacob Astor in New York and had used American Ships to ship NWC furs to Asian markets before.
Thomas Jefferson would have been quite aware of the NWC and its activities in the Pacific North West.
I know from reading about Jacob Astor and Lewis & Clark that many of their crew where French Canadians which makes perfect sence when one reads all of the French names on a map of North America.
However the term Canadian at this time could refer to a French Canadian living any where in North America at the time and these people moved around alot the web site Metis Time Line can be a big help with this.
Amazingly the NWC even manages to continue doing buisness during the whole affair with out skipping a beat by using the Peterborough Route to Penatanguishing.
The French had constructed a ship yard at Point Aux Pins in Sault Ste Marie by 1812 the NWC had some fair sized schooners like: HMS Canadian Fur Trader & Perserverence on Lake Superior.
I think Techumseh probably sailed on HMS Canadian Perserverence to Fort William at 200 tons it was big for Lake Superior but dwarfed by the Ship of The Line HMS St Lawrence far and away the largest war ship ever built on the great lakes.
Some good reads on the subject are The Invasion of Canada & Flames Across the Border by Peirre Burton and Caesars of The Wildeerness by Peter C Newman.
Cheers!
I think Bart has a point though, the War of 1812 was basically a draw. The Brits held the line and the Yanks gained no ground but they did gain grudging respect.
The UK was in no position to intervene in the US civil war and it's support of the Confederate cause was misguided to say the least. John Bright was the lone voice of reason at Westminister.
Geo-politically, the Civil War did encourage the BNA colonies to form a federation but I can't see a single good reason why the Brits would have ever got actively involved in that conflict.