You Do Need power plug adapter while traveling from Brunei to Pitcairn Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Pitcairn Islands is I and in Brunei is G. This is how they look like.

Brunei

In Brunei, outlets of type G are in use.

Type G

Pitcairn Islands

In Pitcairn Islands, outlets of type I are in use.

Type I