Sorry but there is no support for a theory in which economies get boosted by somehow boosting demand. All that does is cause inflation. Even if it is hidden because we stop including things like food and energy cost in the official index.
As mentioned before you are ignoring all of he other rules and regulations that are looser in Australia than the US. We get in our own way in regards to additional costs of employment and operating a business which is the real reason jobs get moved overseas.
Raising the minimum wage is kind of like trying to goose the economy with government spending. Both address the symptoms and not the disease. Its like saying we need more engineers or doctors and fixing the problem by decree instead of actually training more.
We need higher skilled workers whose value to the economy is more so they are paid higher. We don’t get them by forcing companies to pay drive thru order takers as if they were engineers.
Regulations in the US almost exclusively help the largest corporations. Those corporations end up being the ones that hold basic labor costs down because of their monopolistic power over the labor market while paying their executives hundreds of times more. Those sorts of imbalances don’t occur absent that kind of environment which favors the big guys. CEOs of hundred employee companies don’t make that much. That is the larger issue. Though it is more complex so harder to get people to rally behind and the political donors from those big corporations certainly don’t want that status quo changed.