Congrats!!!
Good question, and I'm glad you came here and asked. You'll definitely get a broader spectrum of experience and opinions/answers than at a doctor's office!

Ok, being the father of 4, and with my wife being at WDW during each one, I think I can give a bit of advice on this subject.
My wife has been on just about every ride during her pregnancies (except the Tea Cups - we never ride the Tea Cups). One time she was 9 weeks pregnant and rode everything except Test Track. The last time she was 10 and 18 weeks (two trips - late October and early December of 2007) and rode everything she wanted to. In fact, her midwife rode Tower of Terror 32 weeks pregnant! My wife was too big and uncomfortable to ride most of the thrill rides when we were there and she was about 29 weeks along with our second. Of course, mid-July in Florida and pregnant isn't the best combination for comfort anyway.
It comes down to two things - your comfort level (which really should come before....) and the advice of your doctor. Your doctor is going to probably tell you to not ride anything. Of course, my sister-in-laws doctor told her it was fine to smoke her entire pregnancy (and he delivered our first, her normal OB was out of town the day she delivered). So I think your comfort level is going to be far more important than anything else.
It's normal to be apprehensive - you don't want to hurt your baby!
But at 12 weeks, think of how small the baby is - there isn't much you can ride at WDW that's going to hurt. Personally, I'd avoid Star Tours, Mission: Space, and anything else that would normally make you naseous. What you put into your body is much more important at that point than what you ride.
Hope this helps, and have a great trip!