For most organisations, the choice of structures is between company status and incorporation. Limited companies are highly regulated; incorporated associations are lightly regulated. Setting up a company is complicated and expensive; incorporating as an association is comparatively cheap and simple. Unless your organisation is very big indeed, or carries on a lot of business, your best option will probably be to become an incorporated association.
Incorporation is the cheapest and quickest way to become a legal entity.
Incorporation is a system of State Government or Territory registration that gives an association or community groups certain legal advantages in return for accepting certain legal responsibilities. An incorporated association is a registered legal entity usually for recreational, cultural or charitable purposes with at least five members and all profits applied to the purposes of the association. It receives recognition as a legal entity separate from its members and offers some protection for office holders from any debts or liabilities incurred by the group as long as the association doesn't make a profit for its members.
Procedures for incorporation in each state are set out here for
If you're an association which is registered under a State law that's not recognised in other States - and all the state Associations Acts are of that nature - then you're probably a registrable Australian body. If you're a registrable Australian body, and if you wish to carry on business in other States or Territories outside your home state, then technically you should be registered as a Registered Australian Body under Part 5B.2 of the Corporations Act 2001. This isn't enforced, or even publicised, and you can almost certainly get away with ignoring it, but if you want to be squeaky clean in all circumstances then look into it.
The details of what's involved are on the ASIC site here. The formalities are much the same as for incorporation, and essentially involve you in sending to ASIC the same materials that you have to send to your state incorporation supervisor.