Often "preferences" win!
There are folks who wouldn't tow (what you plan on) with a short bed, or a single rear wheel SRW pickup (gotta be a dually), etc.
So - YOU decide what will work for YOU.
However - you do need a diesel one ton - minimum.
I tow about the same (34') with a 1T '05 Dodge CTD, short bed, SRW.
Works just fine for me - Also, I've had a long bed SRW Ferd Diesel.
(Don't need -or want- a long bed -or- a dually).
A friend tows a much heavier (36') Alpenlite with the same set-up, except it's an '04. He's been back & forth from Alaska (from OR) three times (by road each time) - no problems.
*If* I had an excessively heavy(ier) trailer and felt I *needed* a dually....it would be either a MDT or (singled) HDT, which will tow *anything* you could ever want (or upgrade to).
Either one will "outlive" you, and do most of the other things a pickup will - - for way less money and way more creature comforts, automatic trannys, etc. etc.
A nice used HDT can be had for less than a new pickup, and in most states can be registered as a MH - no special driver's license req'd.
Suggest you visit:
The Escapees MDT and HDT forums, and - since you're in TX -
visit 2L Custom Trucks. He's in TX, and sells lots of MDTs to the horse folks. Sometimes he has some nice pickup & MDT trade-ins.
:C