Since the invention of GPS, there is nothing difficult about flying a light aircraft from the USA to AUS across the Pacific. The FAA are reasonable about issuing overweight ferry permits, so chances are you would want to keep it N registered for the ferry. That has a few ownership issues but is not insurmountable.
The critical part is getting a good ferry tank installation. That's where you really need someone who knows what they are doing. Flying the Pacific these days in a light aircraft is p!ss easy if you know your machine well enough to cope with takeoff weights 25% or more above gross and can stay awake for 20 hours at a stretch, then do an IFR approach in a bit of rain - 'cos it is always raining somewhere on the route.
Paperwork doesn't cause ferry crashes; pilots and fuel starvation do. So get hold of a ferry company or tank installer that knows the score.
If it is your dollar and you are reasonably competent, you absolutely should try to have the flying experience yourself, BUT flying it probably won't work out any cheaper than crating it up and shipping it.
PM me only if you are not just dreaming, because my tank expert contact guy is a busy man.