You Do Need power plug adapter while traveling from Christmas Island to Belize.

Here is Why You Need An Adapter

The outlet and plug type used in Belize are A, B and G and in Christmas Island is I. This is how they look like.

Christmas Island

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

Type I

Belize

In Belize, outlets of type A, B and G are in use.

Type A

Type B

Type G