The dog does make things more difficult. For one thing, you will have problems leaving him alone. Most pet-friendly motels require that dogs not be left alone in a room. Leaving the dog in your car while you shop or grab a meal can be a big issue, especially if the weather is warm. I’m sure you know all the stuff about how fast a car can heat up, even though it’s not super hot outside. All you need is a bystander calling the cops, or, worse, deciding to take action with the tire iron in their trunk.
You may have to hope that Rover won’t bark if you leave him in the motel room to make a quick supermarket run. Or to do all your shopping at the crack of dawn at the 24-hour supermarket, when it’s cool enough to leave Rover in the car. Or, shudder, to get most of your meals at a fast food drive-in.
In campgrounds, dogs generally must be leashed, and you’ll want to do that anyway, to keep Rover from running off to chase a squirrel or something. I frankly don’t think this is the time to try your hand at camping for the first time.
Make you motel bookings in advance. Some pet-friendly places only have a few available rooms, which can book up. Expect to pay a pet fee or extra deposit.
Stop at every possible rest stop. A large dog that can’t stand up much in a moving car is going to get stressed. (I’ve done a long distance drive with a German Shepherd. He was not happy.) You may want to figure out a way to tether Rover in the car, if you can’t crate him, so he doesn’t leap out and run the second you open the door. Or get scared and try to climb in your lap while you are driving.
Be sure Rover is chipped and that you have your vet records easily available, including proof of rabies shots. Rover may be the sweetest-tempered dog on the planet, but a stressed dog, or one that feels obliged to guard your car, can behave unusually and nip someone. Talk to your vet about doggie tranquilizers or doggie motion sickness prevention, if necessary. Look up emergency vet clinics on your route.
I have driven by myself round trip from the Bay Area to Washington DC, roughly the same trip. I took 5 days each way I found that it was 8-10 hours a day on the road, when you build in rest & gas stops. It was exhausting. And I didn’t have a dog with me. I suggest you plot out the fastest route and plan to grit it out.
Don’t forget that ice chest for your food and stuff. You may want to bring some sort of thing to boil water. More expensive places may have a microwave, but you really don’t want to be cooking that ramen in a motel coffee pot.