What were reference ranges for the TSH and Free T4? Were they age-adjusted? I believe they're a bit different for children than they are for adults. Please post the ranges listed on the lab report; those vary from lab to lab so have to come from your daughter's own reports anyway.
Once we see the reference ranges, we can be more helpful.
Does your daughter have any symptoms of a thyroid condition, other than the low weight? Other symptoms could include fatigue/tiredness, constipation/diarrhea, muscle/joint pain, cold/heat intolerance, hair loss, facial puffiness, dry itchy skin, brain fog/inability to concentrate and many others.
Your daughter's Free T4 is at a good place at 56% of its range. Was there a Free T3 test ordered? If not, can you get the doctor or order one, along with another Free T4?
Free T3 is the active hormone that's used by individual cells and is most important.
From my research, TSH is higher in young children than it is in adults and I don't think your daughter's TSH is too high. You should ask to see a pediatric endocrinologist to be on the safe side.