It may not be necessary to have much or any paperwork to export and reimport a rifle barrel to and from Australia. At least that is the case in SA. Don't know about the USA, but I have had shotgun and rifle barrels sent from the USA to Australia with no formal paperwork through the post.
-------------------- John aka NitroX
...
Govt get out of our lives NOW!
"I love the smell of cordite in the morning."
"A Sharp spear needs no polish"