You are going to have to hire a local attorney to assist you with this. The Brevard County Bar Association should be able to give you a referral: http://www.brevardbar.org/
As an aside, you are responsible for keeping your dog contained and liable for any damage he may cause. However, if the facts are as you state them, I think labeling him a "dangerous dog" is a bit excessive. Hire an attorney.
You can try to appeal but I would do so with the assistance of an attorney in your area. However, keep in mind that Florida defines a dangerous dog as not only a dog that has injured or killed a human, but also as a dog that has "severely injured or killed a domestic animal while off the owners' property." Livestock (i.e. chickens) are considered domestic animals per Florida law.
Douglas R. Coenson, Esq.
I agree with my colleagues. You are responsible for anything your dog does, but if this is the only incident of this nature that has happened with him then the authorities' response does seem extreme. Still, they don't know your dog's history, so they have to act based on what happened. A local attorney may be able to help you and the authorities find a less drastic resolution. Good luck...
You should hire a local attorney that does dangerous dog appeals to assist you. You need to appeal the dangerous dog designation. Be sure that you do not miss the appeal deadline. Your chances of success depend upon the jurisdiction, the actual people involved (animal control officers, prosecutor, hearing examiner, "victim," etc); and your preparation. Your argument that he was acting on animal instinct, probably will not assist you.