Why was the defence of Port Moresby so important to Australia's welfare?

It wasn't really. the Japs were completely cut of from their suppliers and it was only a matter of time until they starved to death. However a lot of people were paid for the equipment used and wasted there .

To offer another point of view, the defence of Port Moresby was critical to Australia, because it would have left northern Australia more vulnerable to attack.

Singapore had already fallen, Rabaul (PNG) had already fallen, and the Japanese troops were getting much closer. The threat of a Japanese invasion was very real, as over the period of a year or more, Darwin and northern parts of Australia from northern Western Australia right over to the east, and the Atherton Tablelands, Cairns and Townsville, had experienced periodic bombings from the Japanese.

In May 1942, a Japanese invasion fleet departed Rabaul for Port Moresby, and the Battle of the Coral Sea began. It was a very real threat which was only turned back by the US aircraft leaving from carriers. The Japanese then made their attack via the Kokoda Track, but thanks to the Papua New Guinean natives assisting the Australians and the US troops, the Japanese were turned back, having to retreat to bases at Buna, Gona and Sanananda.

The successful defence of Port Moresby was also a victory for the morale of the Allied troops. General MacArthur had seen some heavy losses, and there have been suggestions that, had MacArthur lost Port Moresby, his career might well have been over.

For more details of the defence of Port Moresby and its importance to Australia, see the related link.