I actually just moved 4 cats and 1 dog over 1000 miles. First, I would never ever fly with an animal that needs to be "checked." It's too risky and I would never feel safe doing it. If it's a small dog that can fit under the seat in the plane with you, then that is an option. With this though, you need to consider that there is a 1 pet per person policy since the pet needs to go under the seat infront of you. So, if you have 4 cats and 1 small dog, you would need to have 5 people flying!
We did not use tranquilizers, but gave my dog dramamine (1/2 pill 1 time per day) becuase she gets carsick (and it made her drowsy) and gave the cats herbal "travel" drops that are suppose to calm them. We were concerned about side effects. If you do go for tranquilizers, make sure to do a "test run" with them. We let the dog ride in a seat (with plenty of blankets and stopped every 2 hours or so for potty breaks/drinks/food) and put all 4 cats together in a small feret crate where they could all lie down comfortably, have food, water, and litter. What we learned is that the cats felt better when they were togther and in a small, enclosed area (we first had them in our large dog crate and they FREAKED; they liked the small one better and we put a blanket over it so only 1 side was exposed). They also never used the litter box in the car (or really ate or drank). If you choose not to have these available, you are suppose to offer them drinks every 4 hours. They can go the car ride without eating.
We actually stopped for 2 nights. All red roof inns are pet friendly. Then, the cats could get out, eat/drink and rest.
Good luck and let me know if you have any questions! It wasn't fun, but they all made it safe and sound!