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

Here is Why You Need An Adapter

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

Bhutan

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

Type C

Type D

Type G

Norfolk Island

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

Type I