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

Jamaica

In Jamaica, 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