A bill of rights defines and restricts the definition of rights and fails to address situations and attitudes as they change over time.
Our common law administered by judges independant of the government already address basic rights and when there is confusion or ambiguity in the Australian law have access to the statutes and principles of international jurisprudence as they relate to human rights. The Marbo case a classic example
If there was a statute of rights established by the Parlament of Australia the judges would not have this ability nor flexibility to oversight the evolution of Australian laws.
The only flaw in our constitutional monarchy is the potential for the Queen to resign as Queen of Australia and we would be stuck with Charlie.
Unfortunately were are storming down the road of a politicised elected president. Already if you ask a random selection of voters who did they vote for the answer, if you get one, would be the name of the leader of their preferred party, not the name of their local representative as envisaged by the drafters of the constitution.