If your daughter is having trouble breathing and has a history of this sort of thing I feel the prednisone is in order. If she takes it now along with maybe some neb treatments she may avoid this cough/croup going to pneumonia. The steroid is not going to cause her any longterm ill effects in this short of dosage, I would definitely give it to her if it was me.
By the way--do yourself a favor and stop reading websites to get medical information like webmd and such! It will only scare you. Long term use of steroids can in some cases cause harm, but this is not the case for your daughter. Personally I would trust the advice of a doctor that has been through med school, treats hundreds of patients, and has physically examined your daughter before I would take the advice of some anonymous web posting that has never met your kid, just my 2 cents...,. There is nothing wrong with doing research so you are informed, but you can't trust everything you read.