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.
Where and for what purposes does your permit entitle you to carry and use a handgun? Is self-defence a lawful reason to possess a handgun? What must you do with the gun when you are not using it?