So long as you believe in nationalism Australia was invaded. the fact that the whole world was simply going through theprocess of becoming smaller as a result of improving technology and transport and weaponry meant that settlement by the technologically superior was inevitable (can you imagine Australia today not being under the control of one power or another). Every person on Earth that moves from one place to another may be described as settling the new abode or invading it. It all depends on how you see the outcome. Never forget the slaughter and rape of Innocent women children and civilians all make up part and parcel of our great historical military and nationalistic traditions. The fact is if it wasn't us it would have been some one else.
Australia started as a penal colony for British prisoners. In the sense that they eventually were able set up a fairly egalitarian industrial society based on English legal principles, the country was settled. But in the sense that they pushed back the native peoples, well, I guess you could on a very PC basis claim part of it was an invasion. But that opens up the whole issue of how settlers in North America dealt with its indigenous native populations and I'm not sure I want to go there.
The debate over this issue is fraught with loaded words like "colonialism" and "invasion" and "imperialism". Even today, historians and scholars are still debating whether countries that wanted to conquer new territories did a good thing or a bad thing-- was America "discovered" or were there native people already living there who were over-run by colonial powers? In some cases, those colonial powers brought updated technology, improved medical treatment, better education, modern conveniences. But in other cases, the native people were turned into a permanent underclass who served their colonial "masters" and could never really gain equality even in their own country. Unfortunately, there is no easy answer to your question. The fact remains that most European countries believed they had a right to explore and take over other countries. We live with the results of that today.
Australia was settled according to British standards. Then it was invaded by the same British as the Aboriginals tried to keep there own standard of living. Pretty much what happened in Australia happened in the USA but not with quite the same amount of bloodshed.
The great flaw in a discussion like this is that writers apply 21st century social standards to 18th century practices and therefore any meaningful answer will never be achieved. We need to accept history as it happened without applying standards.