What plumbing work can I legally do myself in Australia?

Plumbing is licensed for the same reason electrical work is, and the reasoning is public health rather than convenience. Cross connections between drinking water and anything else, and drainage that leaks or vents into a building, cause illness at a scale that individual competence does not solve. So the exemptions are narrow and they vary between states.

Generally allowed

• Replacing a tap washer or jumper valve.
• Replacing a showerhead that screws onto an existing outlet.
• Clearing a blockage with a plunger or a hand auger through an existing opening.
• Replacing a flexible hose on a washing machine.

Licensed work

• Installing, replacing or relocating any fixture, including a toilet, basin, sink or shower.
• Anything to do with a hot water system, including replacing a failed one with an identical model.
• Altering, extending or repairing water supply, sanitary drainage or stormwater pipework.
• Anything connected to a gas supply, which is a separate licence again.

There is one point people underestimate. Flexible hoses under sinks and basins are a leading cause of major internal water damage in Australian homes, and insurers see them constantly. Replacing them is one of the few tasks a householder may do, and doing it on a schedule rather than after a failure is genuinely worthwhile.