and this can be changed by amendment to the Constitution of Canada.
From the
Constitution Act, 1982:
41. An amendment to the Constitution of Canada in relation to the following matters may be made by proclamation issued by the Governor General under the Great Seal of Canada only where authorized by resolutions of the Senate and House of Commons and of the legislative assembly of each province:
(a) the office of the Queen, the Governor General and the Lieutenant Governor of a province; ...
http://www.graa.gov.sk.ca/Protocol/Practice/crown_in_canada.htmIn 1953 Elizabeth II was proclaimed in Canada “by the Grace of God, of the United Kingdom, Canada and her other Realms and Territories Queen, Head of the Commonwealth, Defender of the Faith.” The most recent reaffirmation of the monarchy in Canada is found in the Constitution Act, 1982, which repatriated the amendment of the constitution from Britain. Any change to the position of the Queen or her vice-regal representatives now requires the consent of both Houses of Parliament and of the Legislative Assemblies of all the provinces.
Canadian citizens are not "subjects" of the UK monarch, and have not been since the Citizenship Act of 1947. Citizens of the UK are also no longer "subjects" of the monarch; they are citizens of the UK.
It is about as accurate, and polite, to refer to citizens of Canada, a constitutional monarchy and parliamentary democracy, as "subjects" of our head of state as it would be to refer to USAmericans as subjects of George W. Bush.
Considerably less so, in fact, given the Queen's virtually complete inability, in the real world, to exercise any power whatsoever in or over Canada.