I have a 2010 Dodge 3500 4x4.  I recently bought a 2013 3H LQ . These are the #'s the manf gave me.

GVWR 18,170

Hitch wt  4,170

wt w/3 horses 14,510

empty wt  10,950

I usually haul only one horse and very rarely will I ever haul 3.  So, what do you think? Enough  truck or should I plan to keep the Sportchassis?

Empty weight of 11,000 lbs,  Add your one horse and you are 12,000lbs. I would definitely think you could pull that with a 1ton truck.

Now if you load it up close the GVW of 18,000, You will need the heavier truck.

Painted, that is empty weight BEFORE, all my stuff! Water, clothes, food, hay, tack, scooter, saddle rack, fan, chairs, etc. I figure , by my guesstamation, I should come in at around 14 or 15K. First chance I have to get it on a CAT scale after loading THE stuff, I plan to. As we gear up for retirement, I only want to keep one truck. Now, I just need to make sure which one! LOL!

ps...the 18K weight was the absolute most weight that the mfg says is allowable. I doubt if I will ever come close since I don't put stuff in the hayrack and I rarely carry more than two equine at the most. Usually,  it's me and just one reiner, when the trainer isn't hauling her.

We have an '08 Elite 3H 11' SW with full LQ that we have no problem hauling with an F350 dually.  Based on your empty weight your trailer is a bit heavier.  You must have a longer short wall and/or heavier conversion package.  First stop we made was to the CAT scale.   For comparison our trailer empty weight is 7800# with a 15270# GVWR.  Full tank of water, full tank of diesel, two passengers, 2 horses, and all riding/camping gear:  steer axle 4720#, drive axle 6040#, trailer axle 9460# with a full gross weight of 20220#.  All weights fall within both the truck and trailer limits including CGVWR of 23500#.  Since you already have the larger truck once you get your axle weights you'll have your answer and know which truck to part with.  

Hoss, the Sportchassis making the drive but the dually is easier the rest of the time.