Looks like the closest airport to your destination would be Thibodaux Municipal Airport (L83).
We could do this transport tomorrow afternoon 1/31- pick up in Abilene around 3pm or if the dog can come to Fort Worth we can leave Fort Worth by 2pm. Our trip time from Fort Worth Spinks (KFWS) in Burleson, TX is 3 hours. My wife could meet you to pick up the dog on the west side of Fort Worth (area of I-30 and 820).
We may try to meet another pilot in the Nacodoches/Lufkin area to make the RT shorter since this will be Sunday evening. I will contact him directly.
Alternately we could do Friday 2/5.
Sundie and Greg Ellissundie.firstname.lastname@example.org