Often referred to as USA ESTA visa, the Electronic System For Travel Authorization is actually not a visa, it is an online program for authorizing travelers who are residents of the countries that are covered, including Australia, and approved under Visa Waiver Program to visit the United States. It is mandatory for all the travelers from Australia visiting the US to obtain this kind of travel permit like a visa or an ESTA online authorization.
This is why the ESTA is preferred for visits of up to 90 days or less made either by sea or air irrespective of the purpose that could be business, leisure or medical. Without a valid travel permit, one will be denied to board the plane and to enter the USA. You can apply for Electronic System For Travel Authorization only if you have a legal nationality from countries listed under the Visa Waiver Program. For Australian citizens, you are eligible to apply for the ESTA and can do so now on this website.
If you are planning to travel under the ESTA program it is recommended to apply at least one month prior to your travel in order to have time to apply for a regular USA Visa in case the ESTA authorization is denied.