Visiting overseas Skydivers are covered by Section 3.6 of the APF's Operational Regulations.
In essence, what it means to the overseas visiting skydivers is this:
A visiting overseas Skydiver who holds a valid parachutist's licence issued by an FAI-affiliated organisation may make parachute descents after becoming an APF member and having their skydiving experience and competence assessed by a Chief Instructor.
Australia recognises the FAI Parachutist Certificate and the FAI Sporting Licence issued by your own National Parachuting Organisation. You MUST bring your logbook and license to the drop-zone as the safety officer (DZSO) and the Chief Instructor will need to check them.
Please note that the insurance that may come with membership of your own country's National Parachuting Organisation will probably NOT cover you in Australia.
Drop-zone operators in Australia will require you to take out third party insurance by becoming a member of the Australian Parachute Federation. This is a simple matter which can be handled on any student training drop-zone, and covers you for a minimum of three months.
This means that you should ensure that the first drop-zone you visit in Australia is a student training drop-zone such as Sydney Skydivers and Tandem Cairns.
The Chief Instructor will check your licences and logbook and should endorse your log to the effect that he/she assesses your experience as equivalent to a particular Australian licence level.
You may then skydive and enjoy the privileges of that licence level.
Australian skydive licences run from "A" (lowest) to "F" (highest). Skydivers assessed at "A" licence standard are restricted to skydiving at a training drop-zone. At other licence levels, a skydiver may skydive at non-training drop-zones too.