Councils are NOT government.
“There was a proposal to change the Constitution to formally recognise local government in 1988, and the question was presented to Australian electors in a referendum. Voters overwhelmingly rejected the proposal with every state and territory voting ‘No’. Without the necessary majorities, the Constitution was not changed.
However, when an aspect of government is not mentioned in the Australian Constitution it does not necessarily make it unconstitutional. ” There you go, spell on words.