As others have said, that's a lot of trailer and only the biggest heaviest duty 1 ton duallies comes close. Reality is you are probably looking at Medium Duty trucks for that size.
Now, if you are willing to go 10-12yrs old, yes, you can find 1 ton duallies in your price range. We just picked up a 3/4 ton a little over a year ago for $6k (4door 4wd, good condition) and there were 1 tons available for similar prices, so at $10k you could move up to a diesel.
You don't need 4wd. In fact, it will reduce your max tow ratings.
You may want to go checkout some 5th wheels, I suspect, you will find that something in the 35' range gives you more space than your current rig even though it's numerically smaller.
By the way, if you are shooting for under $10k for the truck, how much do you think a 40' 5th wheel will cost?
