The other thing is that DHL and Fedex don't transport firearms. UPS is the only choice. So you will need to find a local dealer where you are and one in Texas and they will both charge you handling fees, as well as make you sign more 4473's.
Take ANCs advice and transport it as checked baggage. I always put one in the pistol case, empty with the magazines removed (still in the case), and lock the case up and put it in the bag. What will happen is when you check the bag you will need to tell the agent that you have a firearm in the bag and need a check tag. They will inspect it and place a red tag in the lockbox and pass it through. Nothing else is required, although you can bring ammunition with you if it is properly checked in it's own secure lockbox, and that requires further investment to properly make that happen. You'll be able to purchase ammo where you are going so that should not be a problem.
Anyway, have fun.
L-188...I took several weapons to Colorado (COS
) for my brother in law a couple of years ago, and had two rifle hard cases and a couple of pistol cases (his varmint rifle, a shotgun and a couple of .22 rifles for the kids as well as his pistols I had been keeping in the safe). The guys who sat with me on the plane and had worked very hard to impress each with their hunting acumen and weapons skills, while I sat and tried to feign sleep, finally fell silent when I loaded up the baggage cart with the cases. I did not really pay any attention since I was looking for my last bag, when one of them asked me what I was going to hunt, and I said...."Hunt? What do you mean?....." being very serious, because I don't really hunt much. He looked at the cases, and back at me and suddenly developed a real interest in the baggage carousel. I found my bag, looked in it, confirmed I had my own personal pistol case, and went back over the Dollar rentacar with my stuff and those guys all kind of made a giant hole for me and all that crap. It was fairly funny after I realized what they were asking me.
One more thing....make sure you know the firearms laws where you are going. No one is going to inspect your luggage when you arrive, but if you are caught with a firearm someplace where the laws are different than your own state and you have not complied with all local laws you will be letting yourself in for trouble, if caught.