Not too sure about ASIC but the only place I have been asked about it was at Ayres Rock. I reckon if you are flying a non vh registered plane, the chances are you'll be able to get "escorted" access to your aircraft without it. Couldn't be sure though. Maybe ring CASA.
I recently flew a Saratoga from Europe to Australia via Broome (and Thailand for that matter). We had to wait in the plane until quarantine arrived with the spray can. If you have been a bit wooly with your eta (we gave a one hour range because we werent sure about the timing of leaving bali), you might be able to mention to the tower that you're expecting to meet quarantine and customs and they might be able to get them down to meet you. We waited about 20 mins for them. Don't be carrying food in.
For $70, if you have an iPad, I reckon ozrunways would be a great investment for you. With all the charts and Ersa in it, you won't ever be caught landing somewhere without jetA1.
As for places to see, there are heaps but I would say don't miss a low run along the gulf of carpentaria. Beautiful.