War was declared with the British, not Canada.
Yes Canada allied itself, because we were full of loyalists that had left your country, however if you look, there was also a lot of reluctance on their part to turn guns on what they still felt were their fellow countrymen.
Yes you invaded, but it wasn't in answer to any invasion on Canada's part, it was the british -navy- who shocked everybody by leaving their ships and marching inland to burn down the whitehouse. Not Canadians.