You Do Need power plug adapter while traveling from Austria to Monaco.

Here is Why You Need An Adapter

The outlet and plug type used in Monaco are C, E and F 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

Monaco

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

Type C

Type E

Type F