As for the "and export" it is unlikely that many European or American zoos would want to pay to import from Australia when similar animals are available "down the road". So Australia basically becomes an animal consumer, without even the pretence of a breeding program for many of these species. Bit sad, really.
But they do, tigers and red pandas are two species that I can think of where individuals born here are now housed in overseas zoos, oh and gorillas, orangs and silvery gibbons.