You Do Need power plug adapter while traveling from New Zealand to Antigua and Barbuda.

Here is Why You Need An Adapter

The outlet and plug type used in Antigua and Barbuda are A and B 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

Antigua and Barbuda

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

Type A

Type B