Your starting point is too late for PNG unless you go pre-1900. British New Guinea was a colony of Queensland from 1883 onwards, the Australian federal government assuming responsibility for it in 1901 (the commencement of the Australian Commonwealth). It was renamed Papua in 1906. Following its conquest by Australian forces in the First World War, German New Guinea was combined with Papua in 1919.
Had PNG not gained independence in 1975 it would be a colony of Australia. Given that PNG was granted independence at least ten years before it was ready for it, a PNG as a UN trust territory administered by Australia until the late 1980s isn’t particularly unlikely. Beyond 1990 would be very unlikely however; colonialism in any form was well and truly an obsolete concept in Australia by then.