My understanding of the national rules is that if the trailer is < 750kg no brakes are required. Over this and up to 2000kg brakes are required and override brakes are OK. Over 2000kg and electric brakes with a breakaway connection is required. There are also all sorts of complicated rules dealing with Gross Vehicle Mass, tow ball weight, Aggregate Trailer Mass, Gross Trailer Mass & Gross Combination Mass and their relationship to each other.
Interesting that the only variation I can find from the national rules is that WA impose a 100kmh maximum speed limit on any towing vehicle.
What concerns me is anyone with a car license can buy a big 4WD and caravan and tow it anywhere with no training requirement. In fact they can buy a light truck less than 4500kg, hang a 7000kg trailer off the back and tow it on a car license.