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

Here is Why You Need An Adapter

The outlet and plug type used in Falkland Islands is G 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

Falkland Islands

In Falkland Islands, outlets of type G are in use.

Type G