They did invade Australia and it was the militia formations that met them initially and were still there at the final defeats of Gona. Between March and December 1941, the Australian Government moved three militia battalions to Port Moresby to defend this vital northern gateway to Australia. The average age of these militia recruits was eighteen and a half years. Unlike the second Australian Imperial Force (2nd AIF), which had been recruited to fight the Germans and Italians in Europe and North Africa, the military service of the militia soldiers was strictly limited to the defence of Australia and its island Territories. To many in the 2nd AIF, who could not foresee Japan's entry into World War II on the side of Germany and Italy in December 1941, the militia wore the uniforms of soldiers but without the risk of ever being involved in combat. This distinction between AIF and militia service led to the young militia recruits being branded "chocolate soldiers" or "chocos" by some AIF members. The scornful term "choco" was intended to convey a suggestion that the militia recruits would melt if exposed to the pressures of real combat. As if to underline their second class status in the eyes of many senior AIF commanders, the militia recruits were denied adequate training and equipment, and treated with a cavalier disregard for their welfare and feelings. These attitudes produced ill feeling between the AIF and the militia which Australia could simply not afford.
Although initially a volunteer citizen army, following the fall of Singapore on 15 February 1942, the Curtin Labor government ordered full mobilisation on 19 February 1942. Thereafter, all males aged 18-35, and all single males aged 35-45, became liable to conscription into the militia.
During the first half of 1942, the Commander of the 8th Military District, Major General Morris, had no experienced AIF troops under his command at Port Moresby. His main force was the 30th Australian Infantry Brigade, a militia formation comprising the 39th, 49th and 53rd Australian Infantry Battalions. With the exception of the 53rd Battalion, the militia were led by experienced AIF officers and NCOs, but the troops were almost all raw recruits.
Papua, as opposed to new Guinea was australian territory, whereas new Guinea, the northern half of the island, was a protectorate under our control. Militia units could have fought in either part, but were not permitted to leave Australian territory. AIF units were different, and the amendment in Curtins administration allowed that service to be extended to any part of the SWPA command. So it was flexible, but I dont think the Australians would have allowed the SWPA zone to be redefined to allow it to include the central pacific.
After the war, Japan was occupied, it was AIF (which morphed into our regular army) that were used to form part of the BCOF. The main occupation force amounted to 16000 men, all of them Australian, and built around the 34th Brigade. This was a regular army unit.
In the SWPA there were basically four armies that participated
Approximately 250,000 Japanese were sent to fight in New Guinea.
The Australians
When the Pacific War broke out the Australian Army consisted of two parts: an expeditionary force of volunteers called the 2nd Australian Imperial Force (2nd AIF); and the Citizen Military Force (usually known simply as the Militia) which included conscripts and could not be sent outside Australia or Australian-administered territories such as Papua. In December 1941 most of the 2nd AIF was fighting the Germans and Italians in North Africa as part of the British 8th Army. Therefore much of the initial defence of Australia's possessions in New Guinea fell to the Militia units who were not as well equipped or trained as the units of the 2nd AIF. This situation improved as the AIF units were brought back from North Africa and the Militia units were placed on a more professional footing. New Guinea became the main focus of Australia's war effort between 1942 and 1944 and at least 400,000 Australians served there. This does not include forces that remained in Australia. This figure includes large numbers of Royal Australian Air Force and Royal Australian Navy personnel whose planes and ships supported the efforts of the soldiers on land.
The Americans
Japan's conquest of Southeast Asia in late 1941/early 1942 made Australia a vital part of the United States' strategy to defeat Japan. The first advance party of American troops arrived in Brisbane on 22 December 1941 and for the next two years Australia became the main base for American forces in the South West Pacific. By 1943 the American presence in Australia reached a peak of 340,000 Army, but till well into 1943, this figure was well below 50000 men. It included Air Force and Naval personnel. Further not all of these Americans were involved with the fighting in New Guinea many of them did see action there. American engineers and other support troops were sent to Port Moresby in mid-1942 and in September of that year the first American combat units joined the Australians in the battles for Buna and Sanananda, but performed very poorly. it soon became apparent they required extensive further training and many units were sent back to either New Zealand, noumea, or more comonly Australia to receive that training. By the end of 1943 American combat troops outnumbered Australian ones in the New Guinea theatre. In August 1944 the Americans withdrew their combat units from New Guinea in preparation for the invasion of the Philippines and left the Australians in charge of all remaining operations in the area.
The New Zealanders
For the first two years of the Pacific War the New Zealanders fought alongside the Americans in the Solomon Islands while the Australians fought alongside the Americans in New Guinea. However by 1944 bomber squadrons of the Royal New Zealand Air Force (RNZAF) were taking part in air raids against the major Japanese base of Rabaul on the Island of New Britain. In September 1944 the Australians took over from the Americans the responsibility for pinning down the Japanese garrisons on New Britain and Bougainville. While the Americans went to the Philippines the New Zealanders stayed behind to work with the Australians. For the rest of the war RNZAF fighter-bomber and bomber squadrons provided air support to Australian ground forces on Bougainville and New Britain.
Without this massive effort, the japanese would have had much greater freedom to concentrate their land and air based defences around the central Pacific. At Phil sea for example, the Japanese would not have been distracted by events to the south and the American carrier fleets would have been facing at least 3x the numbers of aircraft and around 10x the numbers of ground troops. The americans vey much were relying on the Australians to pin the majority of japanese forces in NG, but the Australians couldnt do this on their own. hence the importance of the SWPA