This has happened to me too, and I find that a lot of it has to do with my posture. Because of my nausea, I find myself slouching forward to alleviate the discomfort, and that's when I get short of breath. If I roll my shoulders back and try to have good posture, I really open up my ribs and I find I can get a much deeper breath.
I have been told by doctors that faintness and shortness of breath can be totally normal during pregnancy, because of the increased blood volume. I also have anemia, so they have offered that explanation for my symptoms as well.
I personally think it's always good to mention these things to the doctor, just so they can note it on the chart in case it starts to get worse, etc. x