Here are the main reasons you would not be eligible: 1  You have not met the eligibility requirements. 2  You have been found guilty of a felony, or pleaded guilty to a felony.
1788: Captain Arthur Phillip establishes a convict settlement at Sydney Cove. Captain Arthur Phillip RN was the commander of the First Fleet of 11 ships that sailed into Botany Bay, New South Wales, in January 1788. Three days later he chose a site at nearby Sydney Cove, in Port Jackson, and on 26 January began to establish a convict settlement.
If he found it to be uninhabited (terra nullius), he was simply to  take possession for His Majesty by setting up proper marks and inscriptions as first discoverers and possessors . In 1770, Captain Cook 'discovered' the south east coast of Australia, landing in Botany Bay. On 22 August 1770, he claimed the whole of the east coast of Australia at Possession Island, naming eastern Australia New South Wales.