To expand a bit on what Ann mentioned.
In the US there are two ways to register a boat.
The first and most common for larger boats is registering with the US
government, managed by the US Coast Guard and properly called
documentation. Non US citizens cannot document a boat in the US and in fact, you must remove a boat from
documentation to
purchase it and take title.
The second option is to register the boat with a state. This process is quick, easy and
cheap. The main complication is each state makes its own rules and the process can very from state to state. The main thing for your idea, none of the states that I know of have any restrictions against
registration by a non citizen. Most states you will have to pay +/- 6% sales tax on the
purchase price but that is a one time charge. The registration fee is annual and can be US$100 or so to several hundred depending on the state. Also a few states charge an annual ad valorem tax on the value of the boat which can add up.
Another caution. I've tried to be an absentee boat owner before and it was a huge pain. I was a lot closer to the boat than you will be from
Australia and tried to get down regularly but frequently left the boat sitting for months at a time. A boat sitting, locked up, unventilated,
engine idle is going to break down a lot more than one that is used regularly.
Corrosion builds up on all the
electrical parts, the
engine gets cranky, the
interior tends to get stale and mildewed.
If you're here a lot, it may
work. But if you're only here 2-3 times a year you may end up spending most of your time on the boat fixing stuff.