The primary problem I see with the plan is the 100+lb trailer. Figure out how to get by with much less - a tent and sleeping pad for the ground weighs ~10-15lbs. Especially if you are enlisting the dogs to pull the weight, it is your responsibility to ensure you aren't overworking them. THe same goes for carrying multiple outfits of clothing so you can 'look nice' - this will contribute to the load for your dogs purely for your own vanity. Two sets of 'bike clothing' (one to wear, one to wash and dry), one off-bike outfit, a couple changes of underwear and some raingear are all you need. Anything else is pure vanity and sounds like it would go completely against the spirit of your trip.
Dogs love to run and love to pull but they don't understand that they have physical limits. They will gladly run themselves to exhaustion to please you, not realizing that you expect them to do the same the next day and they won't be able to manage, or will be suffering. As others have said, the head of midday will be bad for the dogs, so try to cover as much distance in the cool morning or evening.
Also, my experience with touring is that one of the primary obstacles is carrying enough water, and that problem is magnified if you have to bring water for dogs too, although dogs can drink from creeks and puddles if there are any. My experience is also based in Canada, so anything I say about heat and water supplies is at least double in the summer heat of Alabama.
Best of luck!