Bringing your dog? That + food for him will eat up your GVW and take your lift down to 25mm!
What is heavy is the water you will want camping in the desert. 9-10 liters a day with minimal washing and food prep + whatever the dog needs. More than the fuel or the food, that will limit how many days you can enjoy out there before you have to find a town or a faucet. A filter isn't a bad addition, not all the free water you find will be that enjoyable to drink. Also, when it does rain, which happens more in October than most of the year for the Moab area, the dirt turns to grease in a heartbeat. If you have winter chains bring them--sometimes going off the road off-roading is not an option.
Have a great trip! You picked a great route and a great truck-