I don't think I would do it, and I pulled my 3,000 lb. pop-up over 1,500 miles this summer(41 nights camped so far
). You will need a class IV hitch, and I think you would struggle at the smallest of incline.
Maybe if it was just you(wouldn't put my family in that situation) and just going a short distance it could be done. But I can't imagine anybody thinking towing a 7k trailer with a vehicle that is rated at 5k is a good idea.
I know you were asking about with the V8, and I still don't think I would do it. Once you pack up with all you need you get a lot more weight than you think(trust me it adds up quick). So if you have 7.5k tow capacity, pulling an empty 7K trailer with nothing else (camper weights don't usaually account for options such as a/c, propane, bike racks, water((fresh, grey or black)), and everything else you need). You will be far outside of "safe" towing.
Try a hybrid or maybe a Jayfeather TT. Seems like a much better fit.