The big question mark is how well your dog travels. We've got a dog that will just curl up and sleep for as long as we choose to travel - she's done 14 hour non-stop trips with no issues - but I also know dogs that whine incessantly without regular (three hourly or so) stops to relieve themselves and/or have a walk around. This will significantly affect travel time and hence where you'll be able to reach within a given time period.
Other than that, you'll need to confirm that anywhere you're looking to stay is pet-friendly. This may not be as big an issue in the US, but in Australia options are more limited and require researching and booking ahead.
If you're going to go sightseeing the same applies - is the attraction dog friendly? What will you do with your dog while you're visiting the attraction? Leaving your dog in the car can be ok, but it really depends on the dog and also the parking situation (under cover is a minimum) and the weather (never do it on a hot day).
The minimum of travel equipment that we've found is:
- Water bowl and water. You can get a water bottle with a combined drinking tray that is useful for travelling.
- Food bowl and food.
- Something for your dog to sleep on/in, whether it's a blanket or a bed. Ideally it's something familiar to the dog and that they're accustomed to sleeping in.
- Travel harness. This depends on the dog but our's is known to try to hop into the driver's lap - very bad. It also reduces the chance of the dog getting injured if an accident happens.
- The usual leash and poo bags for bathroom stops.