Australia has a lot of foreign businesses and it has a lot of immigrants. Both earn Australian dollars and huge amounts would be sent back their country of origin.
His does Australia balance its books on something like this? How do the economics of it work? Would it lower Australian inflation but shortening the money supply, and raise inflation of the destination country as it prints more money to exchange the Australian dollar?
The other responses are missing this point. This is the right answer. The AUD does not actually leave the country. If money is being sent to America, it is converted to USD first. In theory, the value of USD increases since there is greater demand and the value of AUD decreases. This is the mechanism of exchange rates.
Obviously, it gets a little more complicated than this, but in theory that is what is happening.