You Do Need power plug adapter while traveling from New Zealand to Western Sahara.

Here is Why You Need An Adapter

The outlet and plug type used in Western Sahara are C and E 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

Western Sahara

In Western Sahara, outlets of type C and E are in use.

Type C

Type E