I would never ever leave my dog in my trailer while traveling, nor do we travel with the generator and AC running. We have 3 dogs, and they go in the truck with us or stay at home with a sitter. Depending on the size of your dog, her crate may still fit in the back of the truck either in front or behind your hitch.
But that's a topic that's been discussed over and over on these forums so no sense in beating a dead horse.
Another option for you, maybe, would be a toyhauler RV? They're pricey, but not really once you factor in the cost of a trailer and tow vehicle. These run around 38', but again, you don't have the tow vehicle to worry about. https://www.thormotorcoach.com/outlaw-class-a/
