Hi Nomadic,
I was just recently diagnosed by my own OB/GYN about my hypothyroidism. Had I not gotten my levels tested because of irregular cycles (or lack thereof, 4x a year at most), I would have not necessarily found out. I am also TTC, and I have been for the past year. Your OB/GYN should be able to properly treat you with medication for your thyroid, however, some women opt for an RE in this case.
Regardless, it definitely doesn't hurt for you to ask/question your OB/GYN about treating this herself. I know personally, myself, I am new to this state, and I do not have a personal "family doctor," myself, so I would also not know who to pursue. I would start by asking your OB/GYN if she can treat/handle it (most will!), and then pursue a reproductive endocronologist as Renee said above me.
I am new to this experience as well, and I have been on Synthroid to treat my hypothyroidism for a week now. I am eager to learn whether or not this will help regulate my cycle, so I can make my TTC journey a successful one. Please keep us updated!
