I have a 1996 Chevy Silverado ext.cab Short bed. I have timbrens and add a leaf in the rear as well as 3/4 ton torsion bars. 350ci engine with an automatic transmission. The trailer I am looking at is a 1981 del rol 20' gooseneck. My question is will my truck be able to handle this trailer? I'm new to this so please help me out.

Welcome to the forum...
I hate to be the wet blanket to your party so I'll just list some areas you might look at:

Truck bed length and trailer nose shape. A short bed and a square trailer nose is trouble making a sharp turn. The trailer nose will impact the cab if you're not careful

Bed rail height and the bottom of the trailer's neck-over. Too little clearance will cause a permanent crease or dent somewhere when you drive over up a ramp or a set of RR tracks.

While you have increased the truck spring rate, you haven't said anything about the tire, wheel, axle, bearings. If any piece were to fail, you'll be stuck on the side of the road with a trailer full of horses.

If you're going to haul in any kind of hilly area, the transmission cooling and axle ratio will be critical.

Let us know how you make out with the new trailer.