It's actually an urban legend. While the relative direction and speed of the Earth spinning has a noticeable effect on wind currents and large scale metrics (aka - the coriolis effect), it's so negligible on the scale of a toilet or bathtub to make it irrelevant. Similar to elevation's minor impact on gravity and it's effects on weights and relative time. Other factors such as the way the basin is made, the materials, the curvature, the direction the water comes down, etc. would be exponentially more impacting.
I've never actually been to AUS, but my understanding is that, as you mentioned, the toilet bowls are made in such a way that the water comes straight down and out, as opposed to spinning around the sides like in the US (and elsewhere).
Though urban legend or not, I still like to use it to make fun of Australia 
. That and the fact that they are all just a bunch of criminals.
Well I have had a crap in probably a dozen plus countries around the world and I think it is safe to say that our toilets flush pretty much the same as most European countries as they are based on those designs in the main. American toilets on the other hand where the bowl is half full of water before one starts is a bit disconcerting and I would suggest it is because of this (being half full) that your toilets rotates the evidence before it disposes of it - we on the other hand would rather see it go quickly than watch it do a lap or two of honour first.
