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

Here is Why You Need An Adapter

The outlet and plug type used in Barbados are A and B and in Norfolk Island is I. This is how they look like.

Norfolk Island

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

Type I

Barbados

In Barbados, outlets of type A and B are in use.

Type A

Type B