I've not flown with a head, specifically. But I've flown with coolers of fish from Alaska before. I highly recommend calling your airline, and having them point you to the WRITTEN policy. Follow it to the T. Print it out and bring it with you. If an agent or TSA agent says anything different, you have the policy with you. It at least shows you are trying to follow the rules, and generally results in easier passage than yelling and getting mad (which is what most people do).
As far as hunting- you are going to have a blast. Trust the guide on field judging them, that's the hardest part for a new speed goat hunter. Also, don't let your guide rush you on day 1. Sure, if it's a 75"+ goat in Colorado, you need to shoot it even if it is minute 1. But other than that, this is YOUR hunt. Enjoy it. Make several stalks, get in close if you can, spend time just sitting and watching them. Those funny critters do some wild things if you just sit and watch or get in tight. Don't let the guide rush you to a day 1 kill just because he wants a break between elk hunts. I've seen several guides treat pronghorn hunters like this. Take a couple days if you can, and really enjoy your hunt.
Also, pay close attention to where they cross fences (if that's applicable). They will run a mile down a loose 3 strand barbed wire fence to cross at the exact same point (a slide). Use that to your advantage. Once I cut out the shape of a coyote from a piece of cardboard to keep pronghorn in a pasture I was hunting. I hung it on the top strand over a slide- it worked like a charm. Another time, I hiked 3 miles and slipped in and set up on a slide in the dark, as this group kept bumping as soon as we would drive into the valley. It worked perfectly as the goats walked right in my lap as soon as my partners drove in that morning. I killed a 78" goat, and my Dad killed a 75" goat off that group within hours of each other.
Also, they are much smaller than you imagine. I've seen people flat out miss because they get freaked out with how small a pronghorn looks in a scope. You have to get that out of your mind. I think about it this way- I can consistently put my rounds in about a 3" circle out to X-yards (whatever you personal wall is). So I don't care how much fur is surrounding that circle- if it's and elk or a rabbit, I'm shooting the same size target either way. Just prepare yourself for how small they look in a scope, pick a hair on their shoulder and shoot that hair.
Lastly, when you set up first thing in the morning, wait longer than you think before moving locations if you don't see any. With most other species, they are up and at em as soon as the light is grey. Not so with pronghorn. I find they tend to wait until it is more light before they stand up. I can't tell you how many times I've been standing on a little knob, glassing a huge valley thinking I picked the wrong spot and there are no pronghorn within miles of me. Then, all of a sudden, they start standing up and popping up all over the place- a little later than you think it will be. I think they wait until they can really use their eyesight, which is their primary defense.