To date I have always used John Fleming, US Classic Imports and he ships out of Long Beach.
He uses Western Maritime in W17 St Long Beach and has containers being loaded all the time.
But you cannot ship a car to Australia without an Import Approval, it must not leave the US until this is granted. It costs $50 and is obtained from the Dept of Infrastructure & Regional Development, they want pics, there are different rules going with pre-'89 models but their website has the forms to download.
One snag, you cannot pay the fee online if you use Firefox! Chrome, yes. Internet Explorer, yes. Firefox no!
The vehicles will be subject to GST on arrival.
Ray