You Do Need power plug adapter while traveling from Laos to Bhutan.

Here is Why You Need An Adapter

The outlet and plug type used in Bhutan are C, D and G and in Laos are A, B, C, E and F. This is how they look like.

Laos

In Laos, outlets of type A, B, C, E and F are in use.

Type A

Type B

Type C

Type E

Type F

Bhutan

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

Type C

Type D

Type G