Due in part to Australia’s geographic location, there were few battles that took place in the territorial waters of Australasia during World War II.
There was a German naval group specifically assigned to Australian waters between 1940 and 1943 that harassed shipping. There were also a number of U-Boat attacks against Australian naval forces and merchant marine ships. The most notable of these was the sinking of the HMAS Sydney.
The Japanese also carried out limited military operations against the northern and eastern coasts of Australia. In addition to bombing of airfields and military supply bases, shipping was harassed by Japanese submarines until 1944. In 1942 the Japanese attacked the harbor of Sydney killing 22 sailors in the process and sinking a converted troop carrier. This is the closest thing to a “battle” that occurred in Australian waters that wasn’t an air assault. The largest attack Australian ever endured was the assault on Darwin in 1942, but that was mostly an air attack rather than a naval engagement.