Can a visiting Australian purchase a gun through a transfer agent in the USA for hand carrying back to Australia? Assuming that the Australian has required paperwork and permits to import his firearm into Australia, how does he go about taking possession of a firearm and exporting it from the USA?

It would require a US state department issued export permit to leave the US.

new_guy is correct. There are companies in the USA who do this kind of thing.

I recommend these folks.

Crying Eagle

Thanks, Mike. I'll see what they have to say.

No. Afraid hand carry just isn't possible. There is no way for a 'non-immigrant alien' to legally take possession of a firearm in the US.
Exports can only be done via a US FFL who is also a US State Dept registered exporter. Not many of them left now, due to fixed costs.

Some info:
http://www.losttarget.com/nonimmigrantalien.htm

There's always UPS an Pieces shipments !.

DON'T ASK ME HOW I KNOW !!!.

Get the data, register it at home first, then fly on home with it like you left for holidays with it in the first place!

Should have added, it would only work if you were buying from a friend or private sale in the US not from a dealer.

As I read it from the BATFE website, you gotta be a legal immigrant to purchase here....green card.