Plausability of a Japanese Colony in More Fertile Australia

Say that Australia were more and consistently fertile (like Lake Eyre staying full and stable, wetter seasons, etc.). Would it be possible for a Japanese colony to arise in the land down under? Could they even make it that far before the era of modern ships?

EDIT: Oops, almost forgot. I was wondering how plausible this would be in a time frame that the Japanese are on equal footing with the British. I know Japanese was isolationist for a while as well, so it wouldn't be within those years.
 
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Wouldn't an earlier seafaring Japan be more likely to concentrate its efforts on nearer targets, such as Formosa and the Philippines, instead?
 
Yeah, I was ignorant of all the things inbetween. If the Japanese set sail at an early enough point and began taking the islands one by one over the generations they could make it to Australia in time to establish a presence.
 
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