PLEASE do not give a tranquilizer!! Some airlines even have on their website that this is dangerous - I can't remember why now, but something about their breathing. My vet confirmed it shouldn't be done. I was so worried too when I was taking Pixel to Texas from Florida! I definitely didn't want anyone upset with me for having an annoying little yapper LOL I even told the person next to me how worried I was and I kept looking in his bag checking on him and he would be chewing his new toy (made sure to save it for the trip) and finally the guy next to me said "I think he's doing better than you are" LOL Soon after he went to sleep. On the way back I settled down a lot and he slept the whole entire way. I think the noise from the plane and the rumble of the floor knocks them out
He's been to Texas twice now and we are going back in April again (I have friends out there) and I'm no longer worried (okay, still better knock on wood don't wanna jinx it lol)
Good luck and have fun!