A.V.
I have a fear, too, and it's mostly the lack of control and the TSA, frankly. When I flew the last time, I was most anxious when we were over the ocean and I almost had a panic attack while dealing with the very rude TSA. I tried to be calm and do breathing exercises and I had done my research but missed that they would treat diaper cream like a bomb. They made my child cry and split up my family, which was even more fun. For some reason, though the ocean part of the voyage really bothers me, much more than if I was on a cruise.
But re: the Australia thing...can you try talking to someone who has made the trip? How you get there will also depend on where you are starting from. In my case, I'd be flying across the country, and then over the ocean. I could do a layover to chill for a bit before the next leg.
I would also bring something that would help me sleep. Sleep is a good way to pass the time and help with jet lag. I also held DH's hand for much of the flight, when I wasn't dealing with DD.