As I said, I’m not sure how easy or difficult this is, and it may vary from council to council.
But if you go in with an attitude of wanting to abide by the rules while doing the best for your family, you will get a more sympathetic response from your future neighbours.
Starting from the point of view of “I don’t like your by-laws, I’ll do as I want” will make you an enemy of your neighbours before you’ve even set foot in the door – and probably won’t get you the result you desire.
Google the phrase “assistance dog NSW” and that will open up a whole world of possibilities for you.