If it's only in Texas, and especially this time of year, Chill the meat well before you leave and put it in wax boxes. As far as the cape and antlers, put small pieces of hose on the antler tips to prevent them from chipping or breaking and either freeze, or scrape and salt the cape before you ship it. I would say freeze it and let your taxidermist or his/her tannery do the fleshing etc.
The meat will be fine, but you'll want to make sure the cape is kept cold so it doesn't slip.