You Do Need power plug adapter while traveling from Denmark 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 Denmark are C, E, F and K. This is how they look like.

Denmark

In Denmark, 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