Qatar Airways allow you to convey 1 bird of prey in the economy class lodge of an airplane (a limit of 6 hawks are allowed on every airplane and country guidelines might apply), however no pet canines or felines are allowed in the lodge.

Read here the Qatar Airways Pet Policy and call at +1-888-566-5066 for ticket booking in flight. For USA passengers only.

https://www.one-stophub.com/blog/qatar-airways-pet-policy-usa