No we don't. We have two tiers of Gov and local councils, which is the peoples way of direct negotiation and collaboration between us(our representatives) and big State and Fed Governments. Or at least that is the way it was meant to work when first setup, besides your rubbish pickups. Local councils may pretend to be Gov but never have been and never should be, otherwise we could quickly end up with tyranny.
Representatives are elected to federal and state/territory parliaments and local councils, so that all Australians have someone to represent them at each level of government. Parliaments and councils make laws; governments put these laws into action.
Some of the responsibilities of federal, state/territory and local governments overlap, but generally each level of government provides different services to Australians:
- The federal government has broad national powers. Among other things, it administers (puts into action) laws in relation to defence, immigration, foreign affairs, trade, postal services and taxation.
- State/territory governments have the power to look after laws not covered by the federal government; for instance, hospitals, schools, police and housing services.
- The powers of local councils are defined by Acts of Parliament passed by state parliaments and include responsibility for building regulations, rubbish collection, local roads and pet control.
All levels of government raise money, through collecting taxes, to pay for services provided to Australians. State/territory and local governments also receive some money from the federal government, and states fund local councils.
FEDERAL STATE/TERRITORY LOCAL
The federal government raises money to run the country by collecting taxes on incomes, goods and services and company profits and spends it on national matters: for example, trade, defence, immigration and the environment. State/territory governments also raise money from taxes but receive more than half their money from the federal government and spend it on state/territory matters: for example, schools, housing and hospitals, roads and railways, police and ambulance services. Local councils collect taxes (rates) from all local property owners and receive grants from federal and state/territory governments and spend this on local matters: for example, town planning, rubbish collection, water and sewerage, local roads and pet control.
https://www.peo.gov.au/learning/fact-sheets/three-levels-of-law-making.html
Local government
The six states and the Northern Territory have established one further level of government. Local governments (also known as local councils) handle community needs like waste collection, public recreation facilities and town planning.
The states and the Northern Territory each have many local governments within their borders. The state or territory government defines the powers of the local governments, and decides what geographical areas those governments are responsible for.
The naming conventions for local governments vary across Australia. They can be called cities, shires, towns, or municipalities, but they are still controlled by the state or territory government above them.
In the Australian Capital Territory, the responsibilities usually handled by local government are administered by a department of the territory government.
https://www.australia.gov.au/about-government/how-government-works/local-government
I will cede that local governments do not have recognition in the constitution but they are levels of government created by the states