The British monarch has no constitutional role in Australia and the Queen of Australia has only one constitutional power: the appointment of the Governor-General, which power is exercised on the advice of her Australian ministers. The implication of your report that there may be some vestigial lack of independence from Britain is a frequently encountered misconception.
A republic will eventuate only if a majority of people in a majority of the six states agree at a referendum. It has been notoriously difficult to have radical constitutional proposals accepted by the Australian people, despite the support of opinion polls. Robert Menzies' proposal to outlaw the Communist Party was given 80 per cent approval by opinion polls but failed owing to the common sense of the Australian people.
Chairman, Australians for Constitutional Monarchy