You Do Need power plug adapter while traveling from Norfolk Island to Bhutan.

Here is Why You Need An Adapter

The outlet and plug type used in Bhutan are C, D and G and in Norfolk Island is I. This is how they look like.

Norfolk Island

In Norfolk Island, outlets of type I are in use.

Type I

Bhutan

In Bhutan, outlets of type C, D and G are in use.

Type C

Type D

Type G