Hello Centaurus,
We certainly do have tornadoes in Australia! The response you got from BOM is correct in that they are relatively rare as they are spawned from "supercell" thunderstorms that require a large amount of instability and a quite specific vertical wind profile. The correct conditions exist semi-regularly in the central USA in their spring, but here they are more transient - anecdotally they seem to be most frequent in central Vic and western NSW. You might recall the xmas 2012 storm in Melbourne (which incidentally wrote off my car) was a supercell - this had a radar signature of a tornado and public reports from the area around Bacchus Marsh. Note tornadoes are quite distinct in their dynamics from waterspouts and dust devils, which are associated with convectively forced convergence and can form regularly in quite benign conditions.
What we don't have is a census of tornadic activity in Australia as you need trained spotters and doppler radar coverage to do this well - the problem is that both these only exist in capital cities and there are large swathes of the country not well observed. I know of a couple of researchers look at this at the moment - I'll see if I can dig any results up.
Cheers,
Gareth.