You Do Need power plug adapter while traveling from Cocos (Keeling) Islands to South Korea.

Here is Why You Need An Adapter

The outlet and plug type used in South Korea is F and in Cocos (Keeling) Islands is I. This is how they look like.

Cocos (Keeling) Islands

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

Type I

South Korea

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

Type F