I think that yes the US would have come to the assistance of Australia.
I would think that Japan would have invaded the Philippines on it's way to invading Australia in this what-if since they greatly desired that chuck of land. Since they were still going to attack the Philippines they still needed to hit Pearl Harbor.
But after capturing the dutch east indies, bottling up the British and hitting the US i think that if Japan had launched a concerted attack to invade Australia the US would have launched some sort of relief units to help as soon as they could.
However realistically i don't think Japan had much desire to invade australia being that their motivation to go to war was simply the raw materials of the east indies area, china and india.
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Never, never, never believe any war will be smooth and easy, or that anyone who embarks on the strange voyage can measure the tides and hurricanes he will encounter. The statesman who yields to war fever must realize that once the signal is given, he is no longer the master of policy but the slave of unforeseeable and uncontrollable events. -- Sir Winston Churchill
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