We jump in Australia too,
we have the following events...
Hunter - judged on style, and faults, but the horse with nicest style way of going and least faults wins, the jumps are never raised and there is never a jump off.
Fault and Out - Judged on jump height, doesnt matter how they get over as long as they do and have no faults, one jump not a course, that is continuely raised, up and up, until only one horse remains
Six bar - A set of 6 jumps evenly spaced in a line, that gradually increase in height, the end jump being the tallest graduating down to the lowest being the start jump, the space between jumps is not great, being about 12 feet. This event keeps going the jumps are all raised evenly so they are kept in their gradual raise until one horse is left.
showjumping - like a general showjumping course, big jumps little jumps, keep going and raising jumps till there is a winner!
And yeap we jump in paddock halters =)