Can anybody advise what the rule is regarding shipping an air pistol into Perth
We use the air pistol for competitions only (Pentathlon GB) which is Biathlon and triathlon competitions. Do I need to register it or advise customs ??

From Wikipedia:

Australian laws are controlled and administered by each State and Territory with each classifying 'air', 'CO2' and 'mechanical propulsion' used in air rifles and BB rifles as "Category A" firearms, placing them in the same class as break-action shotguns and rimfire rifles, requiring a licence for ownership. Air pistols and BB pistols pistols are classified as "Category H" for all handguns.

[1] Anyone found in Australia possessing an unlicensed air rifle or pistol faces the same charge as a person who unlawfully possesses a firearm. It is possible in most areas of Australia for an unlicensed person (from age 12) to use a firearm under direct supervision of a licensed person. It is important to check with the State or Territory Police Firearms section as the laws across Australia are not all exactly the same. Air rifle and air pistol pellets are considered to be 'ammunition components' and can only be purchased, possessed and used by a licensed person. The storage requirements for firearms also applies to air guns.

The "Category A" and "Category H" firearm license can be issued to an 18 year old person (or a minor from age 12) after proof of being a member of a licensed shooting club, complete and pass an airgun safety awareness / safe handling and Target shooter obligations course as required by the Firearms law, and have had background checks conducted by the police.

Air gun laws

"It takes at least 6 months to get a firearms license, under WA firearms laws. Pentathletes can still compete at interstate competitions whilst waiting to get a license!"

WA Pentathlon website

WA Police Firearms Licence Application

......unless you are a member of a bike gang, of course <g>.