G'day,
Can't think of any, a lot of miners came from the American gold rush to the Aussie one which occurred a little later. In fact I think that some of the Aussie gold rush activity was started by people who recognized the same signs here that they had seen in California.

Slightly off the question, there is the true story of The Catalpa, an early US/Australia/Irish incident. It's told in these two songs:- The CATALPA and THE FENIANS' ESCAPE

Cheers,
Alan