I can't address what the Australian law is looking for, but I can tell you that rgp is correct as far as the U.S. is concerned.

The Customs Form 4457 is required to lawfully take your firearms in and out of the U.S.

When I went to RSA in 2002 this is the form that RSA specifically asked for and I was told to have when I went down.

The CF4457 use is just as rgp describes. It intended to identify non US goods you already possessed in the U.S.

The Gun control act of 1968 added the requirement for using the CF4457 as proof you had the firearm in the U.S. before you left.