Ok I can help out here. Firstly Australia has 2 Mints. The Royal Australian Mint which is in Canberra ACT and the Perth Mint which is in Perth Western Australia. You may have tried the RAM for info and they would not be able to help because it is a Perth Mint issued coin.
The 2013 Silver Kookaburra $1 one ounce (31.1035g) coin was issued as follows:-
40.6mm Diameter in BU - No Privymark - mintage 500,000 all sold
40.6mm Diameter in BU - Snake Privymark - mintage 50,000 all sold
40.6mm Diameter in BU - F15 Privymark - mintage 15,000 7,600 sold
32.6mm Diameter in Proof - Piedfort High Relief - mintage 10,000, 7,548 sold
Numista did have them all on the one page >>> N#42224
I have just made some edits on the page to show the proof version which is the 32.6mm high relief one.
The Proof one with the different dimensions needs to be moved to a separate page which I will do shortly.
Hope this helps - Mike
Master Referee - See my profile for what I collect.