Johnny...there is no problem buying a boat and getting a STATE registration for any state in which you can establish an address. Be aware that SALES TAXES are due once you register a boat here in most states. Better to register or document it in Australia then move between states so as not to get caught in any of their "nets" ...which usually means no more than 90 days in a given state.
You have an American flag on your Avatar...if you have a US passport you can simply document it with the Coast Guard using a USA address...then follow the "keep moving advice" in the above until you depart from the country. Many counties will not accept state registrations...they will want USA or Aussie documentation.
No longer posting. Reach me by PM!