We move every 2-3 years due to the military and have had at least one pet on every trip. I always worry and plan like a maniac, and the animals always handle it just fine.
Many great suggestions so far, so I will just add some I haven’t seen: call the hotels ahead of time and verify the pet policy. Have that info (when you called, who you spoke to) with you just in case. Unfortunately the policy stated on the website is not always current.
If it’s cold/raining and your dog needs to stretch, stop at a town with a Lowes. Well behaved dogs on leashes are welcome to walk around Lowes - so your pup can stretch his legs without you getting soaked/frozen.
If you have a smartphone, some apps to get: HotelFinder - lets you search for pet-friendly hotels on your route (I used this to book hotels on the fly when our itinerary changed due to a blizzard), Waze - great for navigation and finding rest stops/avoiding speed traps or traffic, and there are a couple of apps for finding dog parks, vets, etc - I think the one I have is called PetMD Pet Services Finder. Hopefully you won’t need any of that but it’s good to be ready for anything!
I have found that even my well-behaved, quiet dog may get anxious and act up when she’s alone in a strange place. We travel with a soft-sided pop up type crate so no one is loose and unsupervised in a hotel room. We also learned to turn on HGTV or Animal Planet if we do leave a pet in the room - seems to help keep them from ‘lonely barking’. (Next time we move will be our first move with 2 dogs - I think we will ditch the crate and DH and I will take turns supervising them and order pizza/take out whenever possible.)
Kong toys full of peanut butter (and then frozen, if possible) are another good way to deter barking if you leave your dog in a hotel room. I think it’s better not to leave them, but if you have to, you can do a lot to ensure that they will behave.
I think a blog would be a lot of fun - even though moving is stressful, it is also a great adventure and a great story to share! Good luck!