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

Here is Why You Need An Adapter

The outlet and plug type used in Brunei is 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

Brunei

In Brunei, outlets of type G are in use.

Type G