Ah, the adventure of flying with pets. Heck, Texas to California is nothing, try doing it from Japan sometime.
Anyway, first, call the airline you are planning to use. Most will allow you to have the cat in the cabin, but she has to be in one of those tiny carriers that will fit under the seat. If she is a large cat, she may not be too comfortable in there.
Also, most also will limit the number of animals that can be in the cabin on any flight,(usually no more than 2) so make your reservations early, and be sure to emphasize to them that you want to have your cat in the cabin. A good idea is to call back about a week later to confirm that they did, indeed, include that information with your reservation.
If you decide that your cat can’t fit comfortably in the under-the-seat type carrier, or your preferred airline won’t let the cat ride in the cabin, and you decide to have her go in the hold, be aware that there are usually temperature restrictions. They won’t let the animal go in the hold if it is above or below a certian temperature. Being in Texas, I would imagine you would run into problems on the upper end of that scale, and they are much stricter about higher temps. than lower.
The restrictions are not because of the temp in the hold itself (it’s temp controlled and pressurized), but because the animal may have to spend some time sitting on the tarmac.
The airline may also require a health certificate. Make sure you find out if they do, and if so, how many days after issue it’s valid (for the particular airline, that is. Many health certificates state they are valid for 30-60 days, but many airlines won’t accept them after, for instance, 10 days)
RE: tranquilizers. Most vets won’t prescribe them these days for pets that are flying. The tranquilizers tend to depress the respitory system, which gets further stressed due to pressure changes in the aircraft. Most deaths of animals during shipping is due to the effects of tranqulizers.
However, if your cat gets as upset as you say, and if you are sure she can go in the cabin with you, you may be able to get a sympathetic vet to prescribe you some. Just make sure you follow the dosage directions precisely. And if you do end up shipping her in the hold, I wouldn’t trank at all.
All that being said, I do want to mention that, though I’ve never had an animal that actually enjoyed the whole flight process, they do seem to recover from it quickly. A few days, and kittie’s trauma will be forgotten.
Oh yes, and Kudos to you for wanting to go to the trouble of taking your pet with you, instead of dumping her at some shelter. The world needs more pet owners like you. Good luck!