We have a Pet (cat) FAK. Mostly human type stuff. We added a squeeze bottle of eye wash. spare collar, leash , self adhearing wrap since tape won't work, small ACE wrap and you need some way to muzzle your pet, a bandana works. Plastic comb and tongue depressors for splinting.
A copy of the Red Cross Pet FAK book fits in the case. A space blanket would be a good idea too.

Dave