The laws in Faroe Islands say the following:
UK driving licenses issued by the DVLA can be used in the Faroe Islands, as well as exchanged for a Faroese driving licence issued by Akstovan.
Source: The Government of the Faroe Islands
It means that:
1. As a holder of a driving license from Australia, you can drive in Faroe Islands without an International Driving Permit.
2. You will not need an International Driving Permit to drive in Faroe Islands with your Australian driving license.