My GP told me I had a very overactive thyroid with antibodies but I wasn't told I had Graves until I saw the endo's registrar or senior houseman or something like that and I don't think he would have told me if I hadn't said to him 'what , you mean like Graves?' If response to something he said. He looked surprised then pointed at me and said 'Yes, Graves, that's what you've got, Graves'
I started on 20mcg and after a month on that had more blood tests and my dose got a letter from my endo (who I hadn't seen at this point) telling me to raise my dose to 40 mcg then after another two months on that I had levothyroxine added as well (block and replace) I had my thyroid Peroxidase antibodies tested at the beginning along with TSH and T4 - T3 never done though.
Sounds like you are maybe booked in to see an endocrinologist and that is who has told your GP to give you the 20mcg carb to start you off - I waited about three months before I got to see an endo. Hope that's some help.