Here is a "guide" to help with wheelbase and trailer length:
http://www.rvtowingtips.com/how-long.htm
It's not law or anything, but it's a good guideline to follow.
If it were me, and that TT was the one my wife insisted upon getting, I would buy a 250/2500 truck. But if you really love your Titan, like someone else already mentioned, you can get a used (high miles) truck just for towing. But then again.....I'd probably just convince my wife that that trailer is just too damn much, then buy something easier for a Titan!

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2006 Nissan Armada LE 4x4, 1993 Toyota Camry LE, 1971 Cadillac Coupe DeVille
Toys: Coachmen 19FLB, Regal 1900 225 hp