To say that PNG seceded from Australia gives the impression that it was a part of the country that decided to become an independent state, which is incorrect.
After the conclusion of WWI, the German colony Neuguinea was made a League of Nations mandate territory under the care of the Commonwealth of Australia. However the start of WWII, the collapse of the League of Nations and Imperial Japanese expansion led to New Guinea being the battleground of a 3 year campaign between the allies led by Australia and the Empire of Japan.
After the surrender of the Japanese in 15 August 1945, the pre-war mandate was reconstituted and remained that way until 1949. In 1949 the Papua and New Guinea Act established the territory as a trust territory of the United Nations that was to be administered by Australia. From that point forward, Papua New Guinea handled it's own domestic affairs while Australia was responsible for it's defence and development. The trusteeship of PNG was never intended to be a permanent status but simply away for a former colony to be developed under the care of a more advanced country until it was ready for independence. It was with that goal in mind that the legislative council of the country was replaced by a parliament called the House of Assembly, which held its first elections on 15 February 1964. In the same year Australia invited researchers from the World Bank to PNG to advise the Australian government on how to best prepare the country's economy for independence .
In the Papua New Guinea elections of 1972, the new government had a nationalist orientation and pledged to bring the country to independence. Due to the new government and the Australian government's eagerness to grant the country independence, self rule was given to the country on the 1st December 1973 and was granted total sovereignty two years later.
To sum it all up Papua New Guinea was never part of the Commonwealth Australia and, Australian control of the nation as a mandate/trust territory was always intended to be on a temporary basis until the country was economically prepared for independence. Papua New Guinea became independent when he did because there was mutual desire for and agreement on independence and it's conditions.
Source:
Papua New Guinea: The Struggle For Development by John Connell.