Even though they are certainly qualified as well, my OB and MFM are happy to let a specialist- my endocrinologist- manage my thyroid levels during pregnancy. Though I always pass on a copy of my latest thyroid lab results to them at prenatal appointments. Some patients prefer working with their OBs or GPs for thyroid issues even during pregnancy.
Right now since I'm pregnant I'm getting my thyroid levels tested once a month (for the first two trimesters). In the past I have had blood drawn for thyroid labs at my OBs office just since it was more convenient than making a separate trip to my endo's office. (But I made sure to pass all lab results onto my endo). For more on thyroid testing during pregnancy: http://www.preeclampsia.org/forum/viewt ... 20&t=44473
I'm hypothyroid rather than hyperthyroid, but I have had a couple of docs tell me in the past that it is better to be *mildly* hyper during pregnancy than hypo. Thryoid disease does raise the risk of pregnancy complications including miscarriage and preeclampsia but treatment seems to lower risks.