You Do Need power plug adapter while traveling from South Korea 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 South Korea is F. This is how they look like.

South Korea

In South Korea, outlets of type F are in use.

Type F

Cocos (Keeling) Islands

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

Type I