Every individual must have a passport if traveling overseas. If you are a dual citizen and want to go somewhere as an Australian, you will need an Australian passport.
For 90 days in a 180 day visa period, Australians who have travelled from one Schengen area to other, don’t need a visa if traveling to another Schengen area. If they go over this amount of time without a valid visa, they can be banned from entering the area or they may pay a fine.