The independent colonies of Australia, chose to come together in one "indissoluble Federal Commonwealth under the Crown of the United Kingdom of Great Britain and Ireland, and under the Constitution hereby established" at the time of Federation.
The Australian Commonwealth is made up of individual states and territories mutually agreeing to continue a measure of self-determination, but also agreeing to share some aspects of government through the medium of a common Federal government. The most effective government is self-government. Government that facilitates freedom is firstly relational, and secondly it only delegates to higher orders of government those duties and responsibilities that cannot be fully dealt with at a local level. The nexus between continuing self-determination and shared common government acts as a protection against tyranny. As frustrating as it is to politicians with an agenda, the Australian Commonwealth has nurtured the freest system in the history of the world.
The self-determining, and independent nation of Australia is also a member of the Commonwealth of Nations, of which Queen Elizabeth II is the Sovereign.