You Do Need power plug adapter while traveling from Brunei to Western Sahara.

Here is Why You Need An Adapter

The outlet and plug type used in Western Sahara are C and E and in Brunei is G. This is how they look like.

Brunei

In Brunei, outlets of type G are in use.

Type G

Western Sahara

In Western Sahara, outlets of type C and E are in use.

Type C

Type E