Most Australian employers and employees are covered the fair work system set up and operated under the national Fair Work Act. Those laws cover companies engaged in trade and commerce together with various federal and territory government bodies. Sole traders and their employees, and most but not all State government agencies who are not regarded by the law as national system employees, such as sole traders and State government institutions. This complex legal system exists because of the Australian Constitution which emereged on 1 January 1901 to create the Commonwealth of Australia.
The general concept of an unfair (or for that matter an unlawful) dismissal is understood by most Austalian employers and employees, and in a sense derives from whether or not an employee has recieved a “fair go all round”, although in the various laws it is expressed in more formal and technical language which makes it a little more complex and legalistic than perhaps it should be.
That said all jurisdictions have very tight time limits, and varying degrees of legal pedantry, so it always pays to crack on and obtain some specialist legal advice as quickly after a dismissal as is possible.