Depression is in fact a well-known symptom of an underactive thyroid [1].
Bear in mind that the reference range doctors use to determine whether your thyroid is healthy is considered too wide by some experts [2] - this will result in false negatives.
The treatment for thyroid disease and resultant thyroid underactivity is (synthetic) replacement thyroid hormone. I'd rather take a replacement hormone than a pharmaceutical drug with its side-effects. Not to mention hypothyroidism is a risk factor for heart disease and more, so better to address it than treat individual symptoms.
[1] http://www.niddk.nih.gov/health-information/health-topics/en...