No, The Reserve Bank of Australia is owned by the Australian Government. You’re taking what you know of the US Federal Reserve and applying it elsewhere.
There’s a separate discussion to be had about the legal structure of the Australian government as a corporation but your specific point is incorrect.
Most countries' fiat currencies and their Reserve banks report to the US federal reserve and are pegged to the dollar system.
The US federal reserve system literally runs these banks and the SWIFT network.
The US federal reserve and what nixon did is literally the asshole from which all fiat, unsound money and federal banks of other countries spring from.
