A nation is made by a population and a territory.
The population should be characterized by an homogeneous culture, well distinct from the neighbouring countries.
It's not because you draw a line on the ground that you can claim "here is Mylandystan, there is Yourlandystan".
So, first of all you should develop a common culture within that piece of land, and try to make sure that it becomes distinctive of that land. Also grow your economy, so that you have an advantage in secession as you can "pay your own bills".
Then, you should seek for reconnaissance from other countries. No nation in the world is going to recognize your new nation just for fun, there have to be really sound economical and political reasons. Then you have two options for secession from Australia:
- pacific way: seat around a table and negotiate a break out.
- non pacific way: brace your guns and fight your freedom against the nasty oppressor.
If you look back at our history, the pacific way can only work when the "oppressor" is too weak (politically and economically) to maintain control over the land, and rather than starting a war which would just make it weaker prefers to sit and negotiate.
Then coming to your second question, your claim that
the more stable a government is, the more it exists
is a practical nonsense. Just as an example, Italy has had a lot of unstable and short lived governments since the end of WWII, while Germany has had a lot of stable and long lasting ones. I don't think Italy has existed less then Germany since then.
Also the concept of stable government is ill defined. Stalin and Hitler, just to give two examples, had very stable governments. Are you aiming for that?
About the last question, how do you grow the population rapidly?
Well, boost your economy, favor immigration (and say good bye to your cultural specificity you just built).