Compatibility summary
You will need a travel adapter in Bhutan; plug types used there differ from Australia.
Plug comparison
Australia plug types: I
Bhutan plug types: C D M
There is no common plug type between Australia (I) and Bhutan (C D M). You need a travel adapter.
Voltage comparison
Australia: 230V, 50Hz
Bhutan: 230V, 50Hz
Voltage difference is within a range many devices tolerate; check your appliance label.