They count everything they have here on election night. The coming back on Monday is to do check counts which invariably find errors (partly why I don't favour counting again and again throughout the night à la the UK). They also have to count postal and dec votes which turn up, and we have until Friday after the election in most jurisdictions to accept postal votes. And then there's the geographical factors to account for.
Most seat results are known on the night in Australia, and for those that are close, you can't move forward with preference distributions for another week, so there'd be no benefit in doing any sort of further counting on the night anyway.
So basically, in Australia we count everything on the night that's worth counting, and if we wanted to be able (for some reason) to declare results on election night or early the next morning, we'd have to make major changes to the electoral system to the detriment of everything else, and even then there's a greater chance of errors.
Potentially there are improvements to be made, but the AEC and Australian elections in general are world leaders and countries like the UK tend, rightly, to ask advice from us, rather than the other way around.