You Do Need power plug adapter while traveling from Christmas Island 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 Christmas Island is I. This is how they look like.

Christmas Island

In Christmas Island, 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