Wyld - PLEASE please please go read stopthethyroidmadness.com/things-we-have-learned
You actually have an above avg doc because they know that TSH > 2 is a problem. most won't treat until TSH is > 5. Actually TSH > 1 with related symptoms is a concern and should be tested further and treated if necessary.
however jumping onto a T4 only medication without extra testing to see what is happening is not the best practice. plus T4 only meds do not work for everyone.
Before medicating she really needs to test for FT4, FT3, RT3, 8am Cortisol, and ferritin + the thyroid antibody tests.