Why didn't the Chinese colonize Australia first?

Question:

Why didn't the Chinese colonize Australia first?

Chinese certainly don't have any problem with migration, so why, over the many centuries didn't they colonize Australia? It was much closer to them than England was. They had the ships to do it. Ghengis Khan and the boys had proved that they can be very roudy and violent. There was an account written many centuries ago about a Venetian merchant (not Marco Polo) who wrote about traveling on a Chinese ship to Australia (e-mail me for more info on that account). I just really don't get it! Australia was extremely sparsely populated by small bands of naked Australoids, so they wouldn't even have to engage in any military conquest either.

Additional Details

5 days ago
I had forgot to mention that I read once where a very large single Chinese ship made it all the way to SE Africa. Also, when I mentioned Ghengis Khan, I was pointing out that they wouldn't necessarily have any moral problem with a conquest of territory. They didn't a real number on Northern Europe for a time, and other regions down to Persia. I'm would not use the current Red Chinese gov't as a measuring stick for Chinse sensibilities though.

Best Answer - Chosen by Asker: 5 days ago
I had forgot to mention that I read once where a very large single Chinese ship made it all the way to SE Africa. Also, when I mentioned Ghengis Khan, I was pointing out that they wouldn't necessarily have any moral problem with a conquest of territory. They didn't a real number on Northern Europe for a time, and other regions down to Persia. I'm would not use the current Red Chinese gov't as a measuring stick for Chinse sensibilities though.