There has never been a King Charles I or King Charles II of Australia, so why is The King known as King Charles III of Australia? 

The question of regnal numbers in different territories has been asked before. 

In 1953, the Rector of the University of Glasgow, John MacCormick, and Iain Hamilton (representing the Glasgow University Scottish Nationalist Association) questioned whether or not the new Queen should be known as Queen Elizabeth II in Scotland, as Queen Elizabeth I had not been Queen of Scotland, meaning that in 1953, Scotland had its first Queen Elizabeth in its history. 

They filed a lawsuit against The Crown arguing that the title of Queen Elizabeth II was breaching the Act of Union 1707; the lawsuit is known as MacCormick vs. Lord Advocate.

The final judgement of the case ruled that regnal number falls under the royal prerogative, meaning that it is a decision that the sovereign themselves can make and that it is not bound by an act of legislation. 

King Charles has chosen to be called King Charles III in all of his realms and territories, including those that were not connected to The Crown during King Charles I and King Charles II’s reigns. This allows for consistency in referencing and helps to eliminate confusion.