I know if this was going on with my daughter I'd insist on a thyroid ultrasound at least. If the pediatrician refused, I'd go to a specialist. I might just go ahead and go to the specialist and skip the pediatrician all together.
of course you need to have an endocrinologist sees her and check all levels, including ultrasound. Does she have any symptoms? like breathing difficulty or swallowing or hard to breath after little exercise or during hard laugh.
A few months back, at one of my schools, I met a 4th grader who told me about how he has a goiter that he gets monitored by an endocrinologist. It was kind of charming that he was so knowledgable and able to speak up about his own situation. Point is, he was seeing a specialist. Maybe that's not a bad idea in your sitation. Hope you get more feedback. Good luck.