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

Italy

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

Type C

Type F

Type L

Cocos (Keeling) Islands

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

Type I