I didn't exercise at all bc I had hyperemesis really bad and ended up on bed rest with preterm labor. I wanted to exercise during my pregnancy, it just didn't work out that way. I read in my parenting magazine and an article in our local paper that said babies born to women who exercised during their pregnancy turned out to be smarter and healthier later on in life. Idk how true it is, but at any rate exercising at any time is healthy for your body.
Just don't overdo it. Keep it light and moderate and don't get overheated. I agree that pregnancy yoga/pilates would be ideal since you haven't been exercising up until this point.
It's fine to work out when you are pregnant. BUT if you haven't been working out already you need to take it easy. You should only work out at the intensity you have been. This wouldn't be a good time to start say...training for a race. You don't want to get overheated. I think things like prenatal yoga, walking, and swimming would be good choices if you haven't been working out much.
I was a runner before I was pregnant and continued to run for a few months into my pregnancy. I then switched to just prenatal yoga/pilates and nice long walks. I gained about 25lbs. I think working out helped me handle labor and bounce back pretty quick afterwards. It is worth trying to stay active!
Best of luck to you!