Of course monarchy is nonsense but I have a thing for pedantry like this.
TBH the nonsensical nature of monarchy works out for Australia, as it costs essentially nothing and sort of acts as a ground strap to make the idea of “head of state” rather irrelevant. Just compare to countries like France or USA where the Head of State gets capital letters and is a person with actual power.
Next best would be a president like in Germany who is basically a nonentity with less power than a GG.