I presume it works on a similar system there as it does here, and you'll find that your bog is connected to a 4" soil pipe which in turn it connected to a 4" stack running vertically and connecting in turn to your main drain.
Piping in anything smaller and your going to cause a 'log jam' and the only way round this is to use a macerator pump at the back of your bog. Something like a 'Saniflo' just be wary of the maximum operating temperature when specifying one of these.