Professor of what? If we're talking law professor than it would behoove you to do extremely well on the LSAT so that you could get into a top school. There are many dual degree programs. Have you thought of a LLM- masters of law? It seems like you're treating law school like it's an "end." There are many other careers that you can pursue other than being an attorney with a JD. The other thing that I'd like to know is what type of law would you want to practice should you become an attorney. There are firms/types of law where you'd need something other than a JD- not just as a preference but as a requirement
It really depends on the school and program, but if you're vigilant you can get through most in 6-7 years. It's a pretty good deal, really, but you give up a lot on both sides to make it work (summer employment, proper TA'ing, free time to work on your dissertation). I'd really make sure you want/need both before taking both on. Perhaps start with grad school, and see how that works out first?
Well that is what is at the heart of it all...I can't decide which one I want to do so I figure I would attempt both.