I have Graves disease. I'm in remission at the moment, but it flared up again during my pregnancy with DD (she's now three months old). In my case, while my levels rose, it was thought (and I agreed) that it wasn't worth going back on carbimazole at the time. My pregnancy was just really closely monitored (which meant I got to see lots of the baby

. It was confirmed she was a girl about five times (I just wanted to be sure, and I was having the scans...)).
When my daughter was born, she was closely monitored to make sure that she hadn't developed thyroid abnormalities in response to my abnormal levels. So far, there haven't been any problems detected. I am planning on a Drs visit soon, it's been playing on my mind that she's growing like topsy (she was only 9lb 1oz at birth, so big but not giant, but now she's huge). I want to check that she's not for some reason struggling with hypothyroidism as a result of the imbalance (I've heard it can go either way). I very much doubt she is, though, as she's very long and tall as well as very plump, I think she's just on good pasture, as people keep telling me.
I know that it's all a bit scary, but don't worry, chances are everything will work out just fine. Graves is very treatable nowdays, and when you're being closely monitored (like it sounds like you are) the risks to the baby are really very small. It's a funny one, Graves, because it's so deadly for both you and the baby undiagnosed, but so easily managed and 'safe' (if that's the right word) when it's been picked up.