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

Here is Why You Need An Adapter

The outlet and plug type used in New Zealand 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

New Zealand

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

Type I