You Do Need power plug adapter while traveling from Cocos (Keeling) Islands to Bhutan.

Here is Why You Need An Adapter

The outlet and plug type used in Bhutan are C, D and G and in Cocos (Keeling) Islands is I. This is how they look like.

Cocos (Keeling) Islands

In Cocos (Keeling) Islands, 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