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

Here is Why You Need An Adapter

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

Barbados

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

Type A

Type B

Fiji

In Fiji, outlets of type I are in use.

Type I