You Do Need power plug adapter while traveling from Mongolia 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 Mongolia are C and E. This is how they look like.

Mongolia

In Mongolia, outlets of type C and E are in use.

Type C

Type E

Cocos (Keeling) Islands

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

Type I