Roverlad,
have a look at
http://www.casa.gov.au/avreg/fcl_lic/overbr.htm and look for licencing --> recogitation of foreign licences - or better still call them up
In the meantime, if you wish to fly for fun or log hours (no training, and no ratings allowed) you can do a straight swap/sign for a "special pilot licence" , you can then hire for pleasure and currency, but no doe rae mee if you get the jist.
You will have to convert, do law , and flight test, and medical.
Class II is usually satisfied by being alive, although the class I is a little more involved, though not as thorough as the JAR class I.
rgds
7g