Queensland has some of the strictest plumbing licensing rules in Australia. There's a long list of work you legally can't do yourself, even on your own home. Get it wrong and you can void your home insurance, lose any sale contract, and face fines from QBCC.
What you can legally do
Replace a washer in a tap. Clear a blocked sink or toilet (using a plunger, hand auger, or chemical cleaner). Replace a shower head or hand-held shower hose where it screws on to an existing outlet. Replace tap handles (the decorative top) where it just unscrews. Replace a flexible water connector on a tap if you can do it without altering the pipe.
That's about it. Even replacing a full tap assembly (where you cut into the supply pipe) is licensed work in Queensland.
What you can't do
Anything that involves cutting, soldering, or joining water supply pipes. Anything connected to the sewer system, including replacing a toilet pan or installing a new vanity basin. Anything to do with gas. Hot water system installation or replacement. Backflow prevention devices. Anything that goes through a wall, floor or ceiling cavity.
Why it's worth following
Two reasons. First, dodgy plumbing causes serious damage. We've seen DIY hot water installs that flooded houses, gas connections that leaked into roof cavities, and burst joins that destroyed downstairs ceilings. Second, your home insurance often excludes damage caused by unlicensed work. Same with sale contracts, an unlicensed install can void the warranty on a brand new hot water system.
What it actually costs
The savings from DIY plumbing are usually smaller than people think. A licensed plumber replacing a tap is $80-$150 including the part. You'd spend $30-$60 on the part yourself plus an hour or two of your time, and that's assuming you don't damage anything. For most jobs, the time saved isn't worth the risk.
The grey area
A few jobs sit in a strange in-between. Replacing a kitchen mixer where you're swapping like-for-like and only undoing flexible connections, technically requires a licensed plumber in QLD even though plenty of people do it themselves. If you're selling or making an insurance claim, errors here matter. If you're staying in the home long-term and you're confident, it's a low-risk job.
When in doubt, call a licensed plumber. The peace of mind is worth the $150.