I have been an avid runner up to getting preggers, and now i am 8 mos along. I did 5K's and all that fun stuff before. When I found out, my doc said I could continue as long as I don't tire myself out and hydrate myself enough. Throughout the months I had to slow down considerably, of course and just listened to my body and did what I could. That would mean jogging some days, brisk walk other days, and mixing it up with the elliptical machine.
According to ACOG they recommend exercise during pregnancy, as long as you don't have risk of pre term labor or have had miscarriages in the past. They also advise that one can continue running as long as they have been doing it before pregnancy. There are pregnant women who have run 5K's and 10K's. I'm not one of them, because I just didnt' want to push myself.
But if one has never run/jog before, than pregnancy is not the time to start. U can go on their official website (ACOG stands for american college of obstetrics and gynecologists) to read up more on exercise.
Those are the current recommendations. Why your doctor prohibits you from running completely, is a bit confusing.. unless you've had preterm labor and pregnancy complications before.
If he says it's unsafe, go with his reccomendations but I'd ask why. U can do alternative things like aerobics, swimming, bike, elliptical, etc. I sometimes do kickboxing DVD's when I can't get to the gym.
Good luck! And congrats!