Has Australia had a revolutionary war?
Actually, it has. The event is generally referred to as "The Eureka Rebellion" or the "Eureka Stockade".
Protesting about unfair laws and heavy-handed methods of law enforcement for rather minor infringements, a large group of miners in the Victorian gold fields declared their independence. Although rapidly defeated in a massacre carried out by forces of the Crown, the rebels made their point and achieved most of the things they sought to change.
The State Library of Victoria has a short precis of those events, which may be viewed via the following link.
https://ergo.slv.vic.gov.au/explore-history/golden-victoria/impact-society/eureka-stockade
Also, an extensive description of the "Eureka Rebellion" may be found on Wikipedia. (All-right - I know it is "only" Wikipedia! However, Wikipedia's account is historically accurate, and provides a comprehensive history of the lead-up to the rebellion, its course, and its aftermath.
While nowhere near as long and bloody as the American Revolution, those who participated in the Eureka Rebellion did indirectly benefit from it. Britain certainly learned from the loss of its 13 North American colonies, and thereafter was quick to grant democratic reforms in its other colonial territories (including what was then the Colony of Victoria).