skorski,
Do yourself a favor and check out all of your steering components.
First have someone turn on the vehicle(in park with the emergency brake on), and lightly move the steering wheel side to side. Not much, just about 10 o-clock to 2 o-clock back and forth. While they are doing that, crawl underneath the front of the truck, and observe what is going on. Each attachment point of the steering should have zero slop. All of the linkage, tierod ends, draglink ends, sector shaft in steering box, trackbar pivot points, should move only in the direction the steering is forcing them to. Any extra movement equals worn components.
Second, turn the vehilce off, jack up one front tire about 5 or 6 inches off the of the ground. Grab your tire on opposite ends, and try to rock the wheel back and forth. If it moves, you possibly have worn out wheel bearings.
Next while the tire is still off the ground, place a long 2x4 under the tire. pull up on one side of the 2x4 while leveraging the tire up and down. Check for slop in the balljoints while you do this.
Finally have your alignment checked. Most alignment shops will say they check all of these points, but piece of mind is doing it yourself. These are all of things one should also check if experiencing any death wobble issues.
If everything up front checks out ok, or is fixed, then you can do some research on some of the aftermarket suspension systems available for your Dodge. Hopefully this helps, and your truck will be more enjoyable to drive in the future.
KP