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

Here is Why You Need An Adapter

The outlet and plug type used in Mongolia are C and E 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

Mongolia

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

Type C

Type E