I think it is uncommon for Australia to move first, but we do move first sometimes. I thought the recent news revenue-sharing laws[0] are an example of that.
> They want EU or US to make a move first to see what works
It's always nice to know how a policy will work beforehand, but I don't think it's remarkable how rarely Australia moves first. Putting aside cultural differences, we're a medium power in a world with many medium powers, even in the West, why would we expect to be first, ahead of European countries, or North American ones, or developed nations in Asia?
[0]: https://www.reuters.com/business/media-telecom/australias-ne...