You Do Need power plug adapter while traveling from Dominica 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 Dominica are D and G. This is how they look like.

Dominica

In Dominica, outlets of type D and G are in use.

Type D

Type G

Cocos (Keeling) Islands

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

Type I