Actually, that's not 100% true. If you are buying and importing a new vehicle, then yes, it has to meet current US safety and emissions regulations. But in a rare case of the government using some common sense, they realize that antique vehicles are most likely being imported for collector reasons, and thus vehicles 25 years and older are exempt from meeting US manufacturing standards.
When I imported a vehicle from Germany last year, I handled the paperwork myself, and hired a vehicle importation company for door-to-door transport. Based on my experience, my biggest suggestion is try to find a company that will handle the entire move. Even though I contracted for door-to-door, what I did not know is that the European company I used only covered the vehicle from Germany to New York, and they then subcontracted with a US-based firm for the US part of the transportation to my house. By far the biggest headache I had was getting the two companies to talk to each other so things could be handled in time before fees and penalities kicked in.
The paperwork was something I could not make heads or tails out of, due to being written in an advanced form of legalese, but fortunately I have a friend who works for an import/export firm, so he was able to walk me through it. If you don't understand legalese too well, then having someone who does will be a necessity in my opinion. Or perhaps you will hire a company that will cover all the paperwork.
There are also three shipping methods to get a car from overseas, a roll-on/roll-off (RoRo) ship where the vehicle is driven onto the ship and chained down with a cargo hold of other vehicles, a shared container where two or more vehicles ship in a single enclosed container, and a private container. I'm sure you can guess which is the least expensive and most expensive options. I went with a shared container as a compromise between security and economy.
And speaking of economy, there isn't any with this kind of a move. You will easily pay the cost of the car a second time just in shipping fees. My move from Germany to Chicago was in the neighborhood of $3300.
Another problem that I never thought of, and will vary from state to state, is that once I got my vehicle, Illinois will not recognize the German title. I got around this in a rather backdoor, grey market sort of way that I hesitate to post on a public forum.
I think my overriding advice is to consider what the vehicle is that you want. Is it something that is unique to Australia, that you really REALLY want, and one is not available here in the US at all? Then it might be worth it to you. But is it something that is also available domestically, that the one in Australia just happened to catch your eye or appears to be a real bargain? Then it most likely isn't worth it, either for the headaches or the finances of shipping it.