Melbourne and Sydney maybe, but Brisbane is drastically cheaper. When I was studying in Brisbane a few years ago my rent was in the ballpark of $300-400 AUD per week for 2-3 bedrooms, even at the higher end of $400/w that's only $1700AUD/m. You can even buy a two bedroom apartment for under $300k in Brisbane, compared to the $1m or more the same would run you in Sydney or Melbourne.
In contrast, when I graduated and moved to Sydney for work we lived a similar distance from the city as we did in Brisbane and yet were paying $500/w for 1 bed and much less total room.
I suspect Darwin, Perth, and Hobart are similarly cheaper. Generalising and saying all our capitals are expensive is incorrect, though I can understand why perceptions are driven by what happens in Melbourne and Sydney since nearly 50% of the population lives in one or the other.
And the populations of the regions around those three cities makes up more than half the population of Australia.
Plus expensive power, fuel, telecommunications, food, etc due to oligopolies in each of those spaces.
What I'm getting at, is that $1000/month doesn't go very far in any of our capital cities (and most people here live in or directly around our capital cities).