This is a very relevant topic. Studies show that doctors have a higher divorce rate than most people, and that is pretty high. Studies also show that when doctors get married to one another their success rate is much higher. Think about it, only another doctor, or other medical professional, will understand the things one must deal with being a doctor, and the hours.
I would not worry too much about meeting someone. From what I have heard, both law and medical school can be swarming with students who need a sexual release from their troubles.
P.S. The reason why MD's get divorced at a high rate is because they are used to making decisions fast and barking orders. The then tend to carry that home and start trying to run their families like their team. Something to think about.