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

Here is Why You Need An Adapter

The outlet and plug type used in Faroe Islands are C, E, F and K 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

Faroe Islands

In Faroe Islands, outlets of type C, E, F and K are in use.

Type C

Type E

Type F

Type K