If by 'their king', you mean 'the king of England'. No, the king of England holds no power in Canada or Australia. However, the king of Canada holds limited power in Canada, and happens to be the same person as the king of England, and it's expected that that will continue as all countries that share that monarch have agreed to the same rules of succession.

Constitutionally, the king of Canada is the commander in chief of its armed forces, provides consent or assent to all laws passed by Parliament, has some immunity from prosecution, and has a pardon power. In actual practice, most of those powers are performed perfunctorily by delegates based on either action by Parliament or by recommendation of ministers determined by the Prime Minister.

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