Does Australia have the moral authority to talk about saving the world from genocide?

No

I'm not sure who does have that moral authority, form an historical perspective... but I think that the basic principle of opposing genocide is sound.

During Australia's early days, many aboriginal tribes were exterminated. There are no aboriginies left from Tasmania, because the settlers literally formed a line across the whole island, and marched north to south killing every single one of them.

I think that an individual, and their words and actions, have to be judged on their own merit. I think that people have to be judged on their own words and actions. If we all had to wear the crimes of our ancestors, then perhaps nothing that we have to say would have any credibility.

we spend more on trying to solve our Indigenous Population problems than Most countries an we have a position in the UN like the rest so yes

They have as much right and moral authority as anyone else. Why not?

why not ????? at least attempt.... versus what ??? doing nothing.... so, Yes.