If you want Dr. Kennedy's thoughts, try posting on the Expert Forum
http://www.medhelp.org/forums/show/132
Coming from someone with hypothyroidism (I'm not a doctor), I can tell you that there are more symptoms than weight gain--thin/brittle hair and nails, feeling cold, feeling tired and sluggish (you can do a search and you may find a more extensive list of symptoms). There are two TSH tests that my endocrinologist runs every 6 months. I suggest you see an endocrinologist and not just your GP--I had three GPs, over the course of several years, dismiss my symptoms and one GP ran a test that was not the TSH test and it came back negative when I really did have a problem.
Best of luck to you and your daughter.