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

Here is Why You Need An Adapter

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

Cocos (Keeling) Islands

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

Type I

Denmark

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

Type C

Type E

Type F

Type K