Thank you for your query,
Your daughter TSH is high and above the normal range for her age.
Continue the synthroid
as advised by her doctor.
The normal range of TSH for her age is 0.7 to 6.4mIU/L. Don't worry about the range war of the lab values and you can discuss your concerns with the Pediatric endocrinologist
and he will guide you.
There may be additional blood work required like testing for anti thyroid antibodies
You can ask for the follow up intervals, her diet any any your concerns.
Hope I have answered your query.