Australians are required to vote. King Charles is the head of state of Australia and should be Australian. He does not vote in elections.
Thus, is he violating Australian law?
He was born in London, UK, which is not in Australia. To be clear, being born in Australia does not make you an Australian citizen of itself, it just means that that the documentation needed to prove citizenship will be different.
There was also a period of time when British citizenship could confer Australian citizenship and Charles was born during that time. However, neither of his parents were Australian citizens. His parents were born in London, UK and Corfu, Greece, neither of which is in Australia.
So he was not born an Australian citizen and AFAIK, he has not subsequently acquired Australian citizenship, nor has he ever become eligible to do so. As such, he is not eligible to vote and cannot enrol to do so.
He lives overseas indefinitely, which would disqualify him from voting even if he were a citizen.