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

Luxembourg

In Luxembourg, outlets of type C and F are in use.

Type C

Type F

Cocos (Keeling) Islands

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

Type I