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

Here is Why You Need An Adapter

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

Palau

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

Type A

Type B

Norfolk Island

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

Type I