Low Ferritin isn't uncommon with Hashimoto's. Ferritin is the iron storage hormone and should be at least 50 - some say it should be higher than that. Without adequate iron, your body can't produce or metabolize thyroid hormones properly.
Have you also had vitamin B-12 tested? It's also not uncommon for those of us with Hashimoto's to be deficient in Vitamin B-12, as well as vitamin D.
Vitamin B-12 deficiency causes a different type of anemia, but has many of the same symptoms as those caused by low iron. You may need to supplement them both. I have Pernicious Anemia (inability to absorb Vitamin B-12 via the stomach) and have to haveinjections to keep my levels up. That makes a huge difference in the way I feel. I had blood work for a recent surgery that indicated a mild anemia so I'm getting ready to follow up and possibly start an iron supplement as well.
Do you have current thyroid hormone test results? It would be helpful if you could post those, along with their reference ranges so we can see your actual thyroid status.
Do you take replacement thyroid hormone medication(s)? If so, what medication(s), dosage(s) and how long have you been taking it/them?
As Barb mentioned, there are sources that recommend ferritin should be at least 100. The following link is to a review of available information on ferritin levels. They concluded that ferritin should be at least 100.
For supplementation, Vitron C is a good source. Each pill contains 65 mg of iron. At your level you may end up needing 2 pills, but I would start with one and see how that increases your level.
Unfortunately most doctors have the "Immaculate TSH Belief" by which they only pay attention to TSH, which is totally wrong. If you want more info, click on my name and then scroll down to my Journal and read at least the Overview of a paper on Diagnosis and Treatment of Hypothyroidism: A Patient's Perspective. You can readily see what should be done for you. You can also give the doctor a copy and ask to be treated clinically, rather than based on TSH. Everything suggested in the Overview is supported with extensive scientific evidence.
If you cannot get your doctor to treat clinically, as needed to relieve hypo symptoms, then let us know your location and perhaps we can give you the name of a doctor in your area that is recommended by other thyroid patients.
Ferritin is considered as a precursor to iron levels. It goes down before serum iron confirms a deficiency. Vitron C will affect both ferritin and serum iron.