You mention Australia, I actually did my first dive there in 1970 and have been diving ever since up until about 5 years ago. It is a fantastic hobby and opens up so many places to you that many only dream about.
I know quite a few people have that feeling the first time they dive with a regulator but It passes very quickly after just a few breaths.
It's exactly the same as breathing with a snorkel but a little easier.
You will be with an instructor who will only be a few feet away and is trained to know that you may "slightly" panic. But only for a few seconds.
In a very short time you will not even realize you are breathing from that piece of stainless steel and it will come natural.
Here in New York where I dove for lobsters hundreds of times from my boat our visibility is almost zero and the most we get is a couple of feet. The first few times I lost my mask I probably panicked a little because I can't find it here, but I know that with just a few kicks, I will get to the surface.
In tourist places where you will probably do most of your diving the water is very clear and you will see your mask or regulator if it comes out of your mouth and it will be no problem.
In a very short time you will be totally enjoying yourself and never thinking about breathing as it will be as natural as you are breathing now.
In the 50+ years I have been diving I almost never heard of anyone getting hurt unless they did something very stupid and I know you are not stupid so nothing will happen to you.
In the tropics my wife would dive with me. This is Tahiti. Notice she doesn't even have the regulator in her mouth. Probably worried about smearing her lipstick.