There are some state variations, but all states require a firearm licence, which has a 28-day wait. They are classed Category B, along with bolt-action hunting rifles. If you are licensed (even an unrelated license such as CCW or blasting permit) you should use that as supporting documentation. A certificate of safety training from an accredited instructor, and membership in a sporting body are helpful too. (Been through it after some years overseas).
Legislation requires a 'genuine reason' for cat A and a 'genuine need' with evidence for other categories. Handguns have the full Cat H treatment which requires a club membership, recommendations from the club and regular competitive match shooting for months. (By the way, that applies even to air pistols).
Antiques are somewhat easier; a M/L single shot made before 1900 is not required to be licenced in most states I believe. However, I also have a collectors licence which means guns held under that licence can't be shot.
If you are an American coming to Australia for sport or work, you should be able to get a temporary permit in advance and bring B/P guns through customs OK, including your handguns if for an international match. Set it up in advance with the stte police through the body you are shooting with in Australia, eg. the SSAA branch hosting you.
State police issue licences, and the form to be released through Customs is a B709A issued by the state police. Usually you would take the guns from customs to the police for licensing, or a dealer for holding while you get the license sorted.
[url]
http://www.ssaa.org[/url].au/ [url]
http://www.ssaa.org[/url].au/newssaa/political%20archive/documentsofinterest/australianz/customs.htm
Which state are you coming to? With that info, you can be better accomodated.