Thanks for your response. When I turn off timezone support, the events are set to be in whatever timezone I'm currently in, so this doesn't help unfortunately.
I've found that selecting "Floating" in the timezone settings for each event does make it so events don't move.

I was wondering if there's a way to change this on all events at once or to set "floating" as the default timezone. Please let me know if you have any ideas.
The best solution I've found it to turn on timezone support, then to select AEST in the timezone option because this was the timezone I was in when I made the events. This is a good temporary solution but will pose a problem if I need to invite others to my events.

It's frustrating there isn't a timezone override option like there is on the iPhone.