You do need a WDH. The Equal-i-zer is a very nice unit as it combines weight distribution and sway control. With one such hitch, the trailer follows the towing vehicle smoothly. Only you will be able to tell, in consultation with your RV dealer, whether your existing WDH can be used.
That sounds like a wonderful trip. ND is a good choice to see all of Big Sky Montana. I90 through South Dakota is a good choice if you want to see the Badlands NP, Wall Drug and Mount Rushmore, all within a few miles. Then you drive West through the NE corner of Wyoming toward Yellowstone NP.