I recall reading that Australian citizens who are ex-military could carry handguns. I'm not sure it that's true or if so, how common it is.
Being ex-military doesn't matter (except for a few people who are considered at special risk because of their service). Any law abiding Australian citizen can apply for a handgun licence. It's not easy to get one, and it can be refused quite readily, but it is possible to do it. Very few people bother. I have but it's less than 1% of people.