You Do Need power plug adapter while traveling from Ireland (Eire) to Bhutan.

Here is Why You Need An Adapter

The outlet and plug type used in Bhutan are C, D and G and in Ireland (Eire) is G. This is how they look like.

Ireland (Eire)

In Ireland (Eire), outlets of type G are in use.

Type G

Bhutan

In Bhutan, outlets of type C, D and G are in use.

Type C

Type D

Type G