Alright, unquoted stuff is my expansion on my quoted points. For the record, all this is stuff I've learnt through studying law at uni/actually reading the constitution.
Commonwealth vs. The States – The Commonwealth’s law is dominant, but Section 51 of the Constitution only gives the Commonwealth power in certain areas.
The constitution gives the commonwealth grounds to legislate on 39 subject matters. Anything outside of these, the Commonwealth cannot enact legislation. If a state has different legislation to the Commonwealth on any of the 39 subject matters as in the constitution, the Commonwealth legislation invalidates (overrules) the state legislation.
The states have unlimited plenary power. They can enact anything. The only restriction is that if a state act is inconsistent with valid Commonwealth legislation, it is invalidated under section 109 of the Constitution.