Canada did not become a self governing dominion of Great Britain until the passing of the BNA (British North American Act) in 1867. So at the time of 1812 it was simply a colony of Britain.

Then in 1931, the Statute of Westminster set the rules for independent governance within the commonwealth, but bound the former dominions to seek consensus on certain matters such as changes to the monarchy. This would have been the first major step towards legislative independence because it laid out the rules of equality among the commonwealth countries and removed the ability of british parliament from legislating on their behalf.

The Statute of Westminster is an important component of common law for commonwealth nations establishing their free-association and eliminating the binding obligations they had formerly as dominions.

The final act of sovereignty came with the passing of The Canada Act in 1982, which patriated the Canadian Constitution and made it illegal for British Parliament to amend Canada’s Constitution.

This was the moment that Canada created both her modern Constitution (Constitution Act 1982) and established the passing of The Canadian Charter of Rights and Freedoms.

Within Canada there is some controversy regarding this due to the dissent of Quebec to sign it into law in Quebec, but a Supreme Court Challenge as part of the creation of the act, also in 1982 upheld that the Constitution was in effect in spite of Quebec’s position.

EDIT: Spelling