The Etihad Airways pet policy is as follows:
Etihad Airways does not permit any type of live animal to fly in the cabin of its aircraft.
Etihad Cargo can take care of the transportation of your pets, horses and other animals.
Falcons are accepted for transportation in the main aircraft cabin and as checked baggage.
In First or Business you’re permitted to carry two falcons per person, or three falcons per additional seat. In Economy, you’re permitted to carry one falcon per person, or two falcons per additional seat.
All other pets are accepted only as manifested cargo and are not permitted within the aircraft cabin or checked baggage.
Taking a pet to a foreign country involves preparation and planning far in advance of your departure date. Requirements for pet travel to a foreign country are set by the destination country. If you are you traveling to another country and bringing along your pet you’ll need to meet the animal health requirements of the country you are visiting.
More information on the Etihad Airways pet policy