A 1960s Japanese fleet trying to invade Australia in 1942

If Japan received a 1960s-style combined fleet on 1 January 1942, could it invade Australia?

It could probably land troops, but conquering and sustaining control over Australia would remain a much larger logistical and strategic problem.

The imagined reinforcement gives Japan jet-equipped carriers, four Yamatos with missiles, and escorts equivalent to the 1962 US Navy on 1 January 1942. Australia's long coastline offers places where this force could probably land troops. Conquering and controlling the continent would require far more than gaining access to a beach. Submarines and the long route around the Philippines and Indonesia would complicate the movement and support of an invasion force. The sudden appearance of the fleet is also expected to reach British and American intelligence networks, prompting a major response. The answer therefore separates the ability to land from the ability to sustain a conquest.