In NSW the local councils have the power to control land use by a state Act, the Local Government Act. The planning powers of the Local council can be over-ruled by the Land & Environment court, which is typically pro-development.
Sunfish nowhere in the Act, Regs or orders does it say where you can build an Airstrip or a HLS - that is not in their jurisdiction.
CASA do, however, define the dimensions, gradients, obstacle free areas etc required.
Local council is the planning Authority that allow you to build a shed, cut down a significant tree, or have a commercial workshop on your land.
no I suppose you don't have to get permission - An occasional aircraft touching down and departing would be a novelty for some - but if it is not sanctioned, becomes regular and the small minds object to it, letters from council will be followed by injunctions from the land & Environment Court.