That is likely way too big for the small coop you have.
What's the diameter of the roof penetration?
Tho those can be good ventilators, it is in no way appropriate for your small coop.
Where in this world are you located?
Climate, and time of year, is almost always a factor.
Please add your...
-Google images of poultry lice/mites and their eggs before the inspection so you'll know what you're looking for.
-Part the feathers right down to the skin around vent, head/neck and under wings.
-Best done well after dark with a strong flashlight/headlight, easier to 'catch' bird and also to...