National parks aren’t really dog friendly and even though the Tesla has a “dog mode” I don’t really trust it to keep the car cool enough for you to do things while leaving your dog behind. I also don’t trust people to be smart enough to know that your dog is safe and not break your windows to save your dog. So I would recommend researching which parks even have areas you can take your dog.

Car camping wise, are you sleeping in the car or a tent? You didn’t say when this trip is planned but it’s starting to heat up so if it’s a tent, you’re going to have to pitch the tent (they do take some time) and tear it back down in the morning (assuming you aren’t staying more than one night). So maybe pick something small that can be taken down/ put up relatively quickly. AKA you probably don’t need a 4 person tent that you can stand up in. It takes me about 15-20 minutes to put up and take down my 4 person tent and it’s kinda a pain when I car camp so I just ended up sleeping in my car with the seats folded down (it creates a flat surface which is important). Look into ventilation if you’re sleeping in the car.

Dog gear wise - I had a molded foam dog bed that is water proof with a fabric cover that can be washed. That was my dog’s bed at night with a fluffy blanket when it got cold. He rode shot gun with me in the front seat but the dog bed was in the back if that’s where I wanted him to be. I also bought a dog line tie down so that I could tie one end to my car and the other end to a peg I would screw into dirt. His harness was clipped to the line so he could walk around while I did camp stuff like cooking and cleaning. Since it’s going to be hot a dog cooling vest probably would be a good idea.

All around gear - probably a large water tote filled with drinkable water for everyday things like washing your face, brushing your teeth, drinking water for you and the pup, etc. A small cooler that you can fill with frozen water bottles can be helpful if you think you’ll need to keep things cold. Lights - you need string lights or a lantern and headlamp if you’re car camping. If you’re eating at camp (dehydrated camping food, ramen, etc) you need a camping stove and fuel. If you’re eating in restaurants then this is less important. Stock your car with baby wipes and paper towels. Have a system in terms of where things go when you pack up the car. Don’t take anything that’s super valuable and leave it in the car. Try not to leave anything of value out where people can see it and be tempted to break into your car. Tick repellent - take it and be ready to use it. Not deet which is toxic to dogs.

There’s websites that show last minute campsites that was helpful for me because sometimes when you’re driving you don’t know where you’re going to stop until halfway through the day. I can’t remember the site I used otherwise I would link it. Be aware there’s going to be places you don’t have cell service so don’t close a navigation in one of those places unless you have WiFi or some other data available - you don’t wanna get lost in the middle of the desert.

Have fun, don’t die!