You Do Need power plug adapter while traveling from Saint Helena 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 Saint Helena is G. This is how they look like.

Saint Helena

In Saint Helena, outlets of type G are in use.

Type G

Cocos (Keeling) Islands

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

Type I