From experience I would disagree with those that suggest you avoid talking to the local council.
OK if all you are going to do is slash a strip and fill some pot holes maybe...
But if your strip involves earthworks, drainage or clearing any native vegetation you might just find yourself in a whole pile of trouble and legal bills.
Rarely will you find an airstrip a prohibited activity so follow the DA process. My experience with Councils (and yes there have been some dickheads) has mostly been positive.
If what you are planning to do is permitted, follow the process!
If it is not permitted there is usually a fair reason, and you need to work around it.