You Do Need power plug adapter while traveling from Montserrat 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 Montserrat are A and B. This is how they look like.

Montserrat

In Montserrat, outlets of type A and B are in use.

Type A

Type B

Cocos (Keeling) Islands

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

Type I