-- Last Updated: Mar-23-13 3:39 PM EST --
I don't know if this is doable or not anymore but you could try retracing Jim Bridgers trip from Bear Lake into Idaho, down Oneida Canyon, through Cache Valley and down to the Great Salt Lake. I think one stretch in Idaho above Oneida is class iV or so, so you might need to move around it. There used to be a book in print with detailed maps and milage. I've done several of the sections but not the whole trip. The lower bear river through Cache valley is kind of a smelly mess - so many dairy farms.
Some info on the heavy duty section ... Walk Around black canyon, definitely clas IV/V and often not passable because of low water.
Green River Wyoming to Flamming Gorge ? The dog still might be an issue. The Green River from the Dam down to Browns hole is nice too. Again I don't know about the dog.
Free Standing Boat Racks