That sounds awesome!

Would it be for the whole year? First I would suggest finding a kind friend to leave the dog with - it is a whole lot of hassle and you don't want her getting lost while somewhere random or getting baked in the car if you get held up somewhere.

School wise, there should be some form of correspondence school that you can enrol them in for the year and then work it as you go. If you condense school down to actual learning time without all the breaks and lunch etc, it is really only a couple of hours a day. It would be easy enough to do that in the morning and then you have the rest of the day free for exploring.