In all states and territories in Australia, it is obligation on the pressure equipment owners to comply with the regulatory requirements.

For example, In Victoria, certain types of pressure vessels and boilers must be registered with Worksafe Authority and inspected regularly.

The registration must be renewed every three years and the inspection frequency shall be in accordance with AS 3788. There are fines of up to $40,000 for person/companies who allow unregistered plant to be used in a workplace. Any pressure vessel or Boilers with a Hazard level of A, B or C as determined by AS 4343 must be registered with Worksafe Victoria and inspected in accordance with AS 3788. This means a simple air receiver or compressed air tank of 100MPa.L (100L x 1MPa pressure or 1000L x 100kPa) will need inspection and registration. 

A vessel containing other harmful gases or liquids under pressure will require inspection and registration at less than 100MPa.L expansive energy levels.

The occupation Health & Safety (Plant) regulations 1995, states that employers have an obligation to ensure that “plant is inspected to the extent necessary to ensure that the risk associated with the use of the plant is monitored.” Worksafe Victoria does not perform mandatory inspections of plant.

It is the responsibility of the owner of the plant to ensure that the plant is maintained in a safe condition and that the necessary inspections are performed.

The code of practice for plants recommends that advice on pressure vessel inspections can be obtained from AS 3788. This standard recommends AICIP certified inspectors as one of the authorities for inspection and certification of pressure equipment.

AS 3788 also provides guidance on inspecting pressure equipment of hazard level D and E. These vessels also need inspection but can be performed in-house. The above stated information has been extracted from the following link
WorkSafe Vic
or search for your plant registration