Unfortunately, the aftermarket never really addressed these trucks and therefore, as far as I'm aware, there aren't very many suspension lift options really available.
Regarding the old 5.5" Tuff Country suspension system you referred to, It isn't designed for your '01 because in Chrysler's wisdom, they decided to ditch the tried and true, recirculating ball steering box in favor of an all new (for 4x4s) Rack & Pinion steering system, beginning in 2000, which can't be raised (at least safely). So, while it's physically possible to install the Tuff Country lift, you'll have to ditch the Rack & Pinion, and rebuild the steering system to use a steering box, which is easier said than done. BTW, Chrysler also changed the front left frame rail, where the box would've bolted on for a "smoother" appearing frame rail which contains no provisions for a steering box.
Other options you may run across online, are those reindexed torsion bar keys. These things are usually advertised for up to 3 inches of lift, but in my opinion, they are a waste of money. (even if they happen to be rather cheap) The problem with the reindexed torsion bar keys is, they do not address the rest of the suspension. And this is critical because, the suspension only has about 3 inches of down travel available before the upper control arm tops out against the bump stop limiting down travel. In all honesty, you'd be better off saving your money and cranking the torsion bars to a maximum lift of 1.5 to 2 inches and at least retain an inch of down travel, which is far better than nothing.
Sadly the only other option for lift is a body lift. I know that most people tend to frown on that idea, but they aren't useless. They do allow the use of larger tires which improves off road capability and ground clearance over smaller tires. Combined with cranking the torsion bars, you can gain 5 to 6 inches of overall lift which will definitely clear 33"s and maybe minor fender contact with 35"s (depending on rim offset)
But this brings up another problem. The Dakota has a pretty small front drivetrain, which isn't suited to bigger, heavier tires. Of course, if your truck never sees dirt, this won't be a huge problem, but if you occasionally off road the truck, you'll be risking some hardware. The front differential on your truck is known as a C208 or also known as an 8" Corporate axle. It was introduced I believe in the 2000 or 2001 model year and was slightly stronger than the Dana 35 which preceded it. The Dana 35 were prone to catastrophically fail when pushed hard off road with tires over 33". What would happen to result in such a failure? In all axles, under load, the pinion tries to move laterally, away from the ring gear. This usually doesn't happen because the pinion is held solidly in place by the axle housing. However, the housing of the Dakota's Dana 35 were made of aluminum and can crack. Your C208 is slightly stronger as it has a bigger ring gear but the housing is still made out of aluminum.
Another weak spot in these axles are the outer wheel bearings, known as unit bearings. These bearings are non-serviceable and supposedly lubed for life. The problem with them is they do not like getting wet. If water gets in them, you cannot purge them out or repack them with fresh grease. The only thing you can do is keep running them till they die, which isn't long after they get wet. Another problem with these bearings is, you must run rims with the proper offset. If you run aftermarket deep dish rims, they create extra leverage on the bearings which shortens their life span. If you can do it, keep the factory rims as they have just the right amount of offset.
If you really want to run 35"s and you're putting in a bigger engine and you take the truck off road, the best option (although expensive) is a solid axle swap. With the SAS, you be using a much better and much stronger axle, which will support your choice of tire size and you can get all the lift you want out of it
6BT, 3200GSK, M&H#3, W/A IC, 5X.012, AirDog100, HE351.