Is your truck a 2500 or 3500......big difference in what they are rated for.
Dodge Truck/Tow RatingsLook up your specific truck and then go get truck weighed 'camp ready' (you, fuel, passengers, stuff etc.) and then compare to weight ratings.
Then you will have a real world idea on how much you have left on each axle, on truck total etc.
With all those dogs.......not plan on staying at many private campgrounds as most have a 2 dog limit.
State/National CGs, Fairgrounds and COE (Corp of Engineers) will be your best as they rarely have any pet restrictions.
OR boondocking (dry camping)
Generators........boondocking yes.