Air Travel With Cat

I might be going to a cat show in Las Vegas with my cat Isis and was
wondering if anyone had any tips on how to travel with her by air. I have
read it isn't good to tranquilize a cat for air travel since it could be
problematic. I have also read that bringing the cat as carry-on and being
able to fit the carrier under the seat is ideal but have no clue how much
room there is under the seat for a carrier. I have a small carrier (not hard
but more sherpa bag-like) but am not sure if it is small enough.

I am guessing the flight will be an hour or so since I'll be going there
from Phoenix. I am concerned that she might need to use the litterbox as
well and I am pretty sure they probably won't allow her out for a bathroom
break. If I also were to fly I plan on bringing her into the vet before hand
so she is checked out and also has her health certificates with me (This is
a new vet so I imagine they'll probably give her a rabies shot and others).

I am also wondering if travelling by car is better or less stressful as a
trip to Vegas is probably at least a 4-6 hour drive by car? I want to do
what is less stressful on Isis. She is ok with car travel short distances
but I am not sure as it is a much longer distance. I also have never been to
Vegas so I am a bit uneasy. Is air travel better than car travel for a cat?
If so, which airline is the best to travel with a cat?

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