Indonesia would look to ASEAN for anything of a largish nature. Although they are really determined be seen as the leader (aligns with their ‘hero’ culture) in any large activity and are more likely to go it alone - they surprised a lot of people when they mobilized a sufficient force to evacuate their citizens from Yemen in 2015.
It is unlikely they would do large scale military activities with Australia - small scale unit-to-unit exacanges and excercises is the extent of it.