According to the printed material obtained from the site within the link:
See illustration below:
In reality there are only two lawful levels (tiers) of government in Australia.
The first being federal (Commonwealth), then state/territorial (also known as 'local government' - as defined in the document called 'Australia's Constitution').
What is referred to today as 'local government' or city councils is referred to as municipal office, a department of the state, and NOT another level or tier of government.
See page 936 (illustration above) of the document called "THE ANNOTATED CONSTITUTION OF THE AUSTRALIAN COMMONWEALTH" By John Quick and Robert Randolph Garran, in the link below which is a digitised version of the book from the University of Toronto Library, Canada. (1056pages, 76.5MB)
Australia's 'founding' document is the Australian Constitution which came into effect on 1st of January 1901.
Available for download in the link below is "An Act to constitute the Commonwealth of Australia" with the lawful seal, which contains the Constitution from Section 9.
Another piece of misinformation brought to you by the (trusting?) government.