You Do Need power plug adapter while traveling from Faroe Islands to Cocos (Keeling) Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Cocos (Keeling) Islands is I and in Faroe Islands are C, E, F and K. This is how they look like.

Faroe Islands

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

Type C

Type E

Type F

Type K

Cocos (Keeling) Islands

In Cocos (Keeling) Islands, outlets of type I are in use.

Type I