You Do Need power plug adapter while traveling from Saint Kitts and Nevis to Norfolk Island.

Here is Why You Need An Adapter

The outlet and plug type used in Norfolk Island is I and in Saint Kitts and Nevis are D and G. This is how they look like.

Saint Kitts and Nevis

In Saint Kitts and Nevis, outlets of type D and G are in use.

Type D

Type G

Norfolk Island

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

Type I