One amusing consequence is the US might actually ''conquer' Canada. The war was the cause of a wave of Canadian patriotism. Without that, regular interactions, commercial and personal, would lead to closer relations. Patriotism towards BRITAIN was significant, but a little distant. The was little patriotism towards the Family Compact, the small clique who ran Canada.
So, without the war, practicality, and a desire for a political voice might well have led Ontario, at least, to join the US. With the war (OTL), that possibility disappeared.
So the War of 1812 may have been the best thing to happen, for Canada.