It will be fine. I took a couple of kegs to Cincinatti and back this year. The hot car was the only issue- I had to keep my car locked for a few days on the trip down, and it was really hot. The beer was ok, but not as good as it was before the trip. Still, moving it wasn't the problem and your beer will be fine on the trip.
I would force carb, not prime it. The reason is just my preference- you'll have some trub stirred up anyway. If you prime, you'll have way more stuff to stir up again.
You'll be drinking green beer if you're planning on drinking by August 29, though, if it's fermenting right now.