Most states the process is conducted entirely on-line and within a few hours.
Some states do charge a fee, (NSW I think is around $25)
Vic takes the longest as far as Im aware as these are still dealt with through the postal system. That said they have improved their system and now accept permit applications through email but send the paperwork to you by post.
QLD system looks a little more complex on the surface but thats simply because of the structure. Once the permit is accepted (if importing into QLD) the documentation has to be sent to the seller. 2 parts of that documentation stay with the seller and the other 2 must accompany the animals/s in transit.