Is it legal to cut vegetation in Queensland? IIRC it is illegal to cut down anything at least in Victoria, even a dead standing tree.
I don't know about the legal question but I would try to avoid cutting down any plant unless I can identify it as a pest species. Privet, lantana, etc. etc.
In some places I explore in the bush there's an enormous amount of fallen logs and sticks, so I would try to use them to build something.
If I really needed green wood I would try to only take a branch, so the rest of the tree keeps growing. Or if I absolutely need a tree trunk I would try take it above the lowest branch, because many plants should stay alive and re-sprout.
Also when taking green leafy vegetation such as palm fronds I would try to only take a few from each plant, making sure 3/4 of the fronds are left in tact.
I'd do my best to follow these principles even on private property where I have permission to use the natural resources.
Fairly sure it's possible to build a hut without cutting down any trees, at least in some places.