In certain cases, monkeys, cats and even miniature horses may qualify as service animals; however, the airlines can specify that they will not permit in-cabin transport of service animals other than dogs. Additionally, there may be restrictions if the service dog is recognized as a dangerous breed.

The DOT has permitted the airlines to restrict the species of animals that they will accept as service animals. Several airlines restrict species such as amphibians, reptiles, rodents, ferrets, goats, hedgehogs, insects, snakes, spiders, sugar gliders, farm poultry, waterfowl, game birds, birds of prey, animals with tusks, horns or hooves (excluding miniature horses) from flying as emotional support animals.

https://www.pettravel.com/passports_comfort_ani...

Yes