I was actually diagnosed with Hashimoto's Thyroiditis when I was nine years old. My mother is a nurse and works for our city's health department. She started to notice that I was not acting like a normal nine year old kid.My twin sister started growing much taller than me and my growth seemed to stop. I was forgetting my math facts in school and everyday when I came home I would lay down on the couch and fall alseep. I always remember my mom waking me up for dinner and me wanting to do nothing but sleep. One of the major symptoms I did not present was weight gain. She recognized the symptoms right away and took me to an endocrinologist as soon as possible. So it's not to young of an age to be diagnosed with a thyroid disorder because anyone can be diagnosed. Your best bet is to have her levels checked again.
Sorry to hear that your daughter is suffering with the effects of Hashi's. I am glad to hear that the doctors have started her on meds. I was surprised with the starting dose. It is far better to start cautiously and increase as the patient becomes acclimated with the meds. A heavy starting dose risks a reaction not unlike that of being hyper, which of course is very uncomfortable.
It is good that your daughter was tested for FT4, along with TSH, but she should also be tested for FT3. FT3 largely regulates metabolism and many other body functions. Studies have shown that FT3 correlated best with hypo symptoms while FT4 and TSH did not correlate. If the doctor resists testing for FT3, just insist on it and don't take no for an answer. It will be even more important to monitor FT3 as your daughter continues to increase meds to offset the loss of natural thyroid production.
Many members have gone through Hashi's, since it is the most common cause of hypothyroidism. Many doctors treat Hashi's by waiting until symptoms become very overt. Others prefer to start earlier with meds. You can read about that in this link.
http://thyroid.about.com/od/hypothyroidismhashimotos/a/preventative.htm
The most important thing for your daughter is to find a good thyroid doctor. By that I mean one that is willing to treat her clinically, by testing and adjusting FT3 and FT4 as necessary to relieve symptoms, without being constrained by resultant TSH levels. Symptom relief must be all important for her, not just test results. Test results are valuable mainly as an indicator during diagnosis, and then afterward to monitor FT3 and FT4 levels as meds are increased toward symptom relief.
I think you can get a good idea of the clinical approach by reading the letter in this link. It was written by a good thyroid doctor for patients that have consulted with him from a distance. The letter is sent to the PCP of the patient to help guide treatment.
http://hormonerestoration.com/files/ThyroidPMD.pdf
Regarding testing, since she was only on the 150 mcg dose for two weeks her blood levels would only reflect about 75 % of the actual dosage amount. Likewise, most of that will have dissipated in two weeks after changing the dosage. Any time after that you should get a reasonable look at her thyroid hormone levels. When you do go back for re-test, that would be a good time to insist on the FT3 test, along with FT4 and TSH. Down the road, further testing would be advised, since hypo patients often have deficiencies in areas of Vitamin A, D, B12, iron/ferritin, and selenium.
When you get further test results, please post them, along with reference ranges, and members will be glad to help interpret and advise further.