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

Réunion

In Réunion, outlets of type C and E are in use.

Type C

Type E

Cocos (Keeling) Islands

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

Type I