Be very, very cautious!! Your doctor is wrong and clearly doesn't understand CFS. The primary identifying characteristic of CFS is an intolerance to exercise, something the CDC euphemistically calls "post-exertional malaise" (which is much worse than it sounds). When you have CFS, any kind of exercise or exertion can cause a sudden, severe flare-up or "crash". Anywhere from 1 hour to 24 hours after you exercise, you suddenly feel as if you have the flu.
For this reason, people with CFS must be extremely cautious about exercise. being completely sedentary isn't good, either, but you need to figure out what your limits are and carefully stay within them to avoid crashes.
You should especially avoid aerobic exercise, where your heart rate increases, because people with CFS have dysfunctional metabolism and cells that don't handle aerobic exercise well, causing something called oxidative stress when you over-exert (which is what causes the flu-like feelings).
The best thing for most people with CFS is a very gentle program of slow, relaxed yoga or other stretching, combined with slow, short walks. It may take awhile to figure out how much you can handle without crashing. For me, I can walk slowly for about 20-30 minutes on a good day and can't handle any exercise at all on a bad day. On a good day (though not in the same day!), I can also handle about 30 minutes of gentle yoga, but a full 60-minute class is too much for me (I use a video at home). For some people, physical therapy is a good approach - but only if you can find a physical therapist who understands the exercise intolerance of CFS.
Here is a good explanation of CFS, including the exercise intolerance, from the CFIDS Association of America:
Here's an excellent article about exercise in CFS which summarizes some of the research on this topic:
Whatever you decide to do, take it very slowly and gradually. I hope this helps. Please feel free to contact me again if you have additional questions or concerns.