ASIC: unless this has changed over the last three years, the ASIC card cannot be mailed out of Oz, it needs to go to an Australian address AFTER you have cleared immigration.
In your scenario this means one of two things:
1) If you plan to travel to Oz any time before your private flight then apply for it now and have it mailed somewhere you can pick it up in Oz. You then arrive ASIC in hand
2) Apply for it beforehand, but know that you won't have it for the first part of your trip and plan accordingly.
One thing you should really do on your way back is to fly along the Great Barrier Reef. Spectacular
