I think you will find it will firstly depend on the zoning, and even then many councils require a Development Application even for Rural zoning.
For occasional private operations they will usually be most focused on environmental issues these days such as not clearing native vegetation to build your strip, water run off, noise if in proximity to neighbours, and approach paths over other people's houses or livestock etc
For agricultural & commercial operations it gets a bit more onerous.
Just a tip though check local definitions of what constitutes an airstrip. In some councils I saw a few years ago landing in a paddock was OK provided you did 7 movements a month or less. 8 movements it became an airstrip which triggered the DA.
I did a project last year that included building a private airstrip (albeit one to be used for joy flights) in a very sensitive environmentally protected area that involved the clearing of protected native vegetation. We got this approved by aligning it with an existing public access road... in effect just widening the road clearing... and by planting only native grasses and developing a management plan to ensure the strip surface had grass cover to prevent erosion and to manage weeds... and we got Rural Fire Service onside by offering to make the strip available FOC in case of bushfires. The most difficult part was the design of the septic system for the toilet in the hangar because the location was in a drinking water catchment.
It will help if you do your homework before contacting the local council and have the answers before you even talk to them.