How Do I Find Someone Who Moved To Australia?

You can check with your country's relevant department whether they are
ready to provide you information on that. Also first try contacting
your friend's relatives and friends you know either on phone or in
person. I have found for you following websites which claim of finding
someone in Australia, Since you are not in Australia I think they can
be of help to you in Australia. Take a look at:

Search Dear Ones In Australia,

And

Search People In Australia.