Most states treat a dog injuring another dog as property damage and leave you to prove ordinary negligence. Florida has a statute that says it directly.
Section 767.01: “A dog owner is liable for any damage done by the owner’s dog to a person or to any animal included in the definitions of ‘domestic animal’ and ‘livestock.’”
Your dog is named in that sentence, not squeezed into it by analogy.
What is recoverable is narrower than people hope. Veterinary bills are the core of it. Florida courts have generally been conservative about emotional distress damages for injury to an animal, so the realistic claim is usually the treatment cost, and that is worth being straight about before anyone spends money pursuing it.
Two other things are often worth more than the money. First, an attack on your dog can support a dangerous dog classification — § 767.11 includes a dog that has “more than once severely injured or killed a domestic animal while off the owner’s property.” Second, if you were injured yourself trying to separate them, that is your own personal injury claim and it is a different and usually much larger one.
Report it to animal services either way. It creates the record that the next incident will be measured against.