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

Here is Why You Need An Adapter

The outlet and plug type used in South Africa are C, M and N 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

South Africa

In South Africa, outlets of type C, M and N are in use.

Type C

Type M

Type N