The right to silence is not protected by the Australian Constitution, unlike in the United States where is is guaranteed by the Fifth Amendment to that nation's constitution and reflected in what are commonly known as ‘Miranda rights', also known as the right against self-incrimination.
Rather, protections against a person's silence being used against them in criminal proceedings have developed in Westminster (British) common law – which is law developed by the courts over many years.
Here's a general outline of the current protections in states and territories across Australia, as contained in laws and crystalised in formal cautions given by the police.
What is the right to silence?