You Do Need power plug adapter while traveling from New Zealand to Saint Kitts and Nevis.

Here is Why You Need An Adapter

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

New Zealand

In New Zealand, outlets of type I are in use.

Type I

Saint Kitts and Nevis

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

Type D

Type G