Well no real mountain ranges in the way
It is rated as 1/2 ton truck so 1,000lbs limit in bed, that needs to include the weight of the canopy.
Look at your trailer hitch, it should have the tongue weight and towing weight listed.
2.3l Ranger is not recommended as a towing vehicle, and you probably won't be able to rent a trailer for one-way hauling.
And as odd as it sounds manual trans vehicles have a lower "allowed" towing weight than automatics.
Look at the drivers door for the AXLE code, then read here:
http://www.therangerstation.com/tech_library/axle_codes.shtml
Many 2.3l Rangers were sold with axle ratios under 3.73, this makes towing very hard, but makes MPG very good, the reasoning is that someone buying a truck with 4cylinder engine wanted better MPG not better towing.
So look up your axle ratio, 3.73 or higher is good, 3.55 or lower not so good.
Can you do it, sure, but you could breakdown or wear out the truck so much that it requires new clutch or other parts when you get to Texas.
Just to have a price point I would contact moving companies that offer PODS or similar containers that you can load up and then these are transported from point to point.
If you are flexible with delivery dates it isn't all that expensive, and it is insured.
Then just take what you need in the truck.
23 year old truck will have breakdowns just in general use, but if it happens "on the road" it can get expensive even for simple repairs, and with a trailer it complicates things, i.e. you don't want to leave it at the side of the road, even for an hour or two, especially if it is an open trailer.
So just look at other options and see what makes the most sense(cents)