Compatibility summary
You will need a travel adapter in Cayman Islands; plug types used there differ from Australia. Voltage differs by more than 20% — a voltage converter may be needed for some appliances.
Plug comparison
Australia plug types: I
Cayman Islands plug types: A B
There is no common plug type between Australia (I) and Cayman Islands (A B). You need a travel adapter.
Voltage comparison
Australia: 230V, 50Hz
Cayman Islands: 120V, 60Hz
Voltage converter recommended (Australia 230V vs Cayman Islands 120V).