Hi sorry your dog is having problems.
This could be anything from Kennel Cough to heart problems. You do need to see your Vet….please inform them she is coughing when you make the appointment though as if its possibly Kennel Cough they may see her outside as its very contagious.
I would talk to her doctor but, in general birds have the most airborne allergins of any animal. So, in short, no I wouldn’t think the no cockatiely