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

Austria

In Austria, outlets of type C and F are in use.

Type C

Type F

Cocos (Keeling) Islands

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

Type I