You can ship handguns across state linesvia UPS to a licensed dealer (must have an FFL) who will then complete the transfer by having the buyer complete the required paperwork (state & federal transfer forms, background check). I've bought several pistols and rifles online in this way.

Like the others recommended, try selling it in your state first. I don't know exactly how Texas' handgun laws are written, but generally, private sales between individuals are allowed without any third party involvement. Checkthe State Code and/or speak with an FFL to get the info.