It all depends how low your iron is. Do you know your ferretin level? If not, each time you get a blood test get the doctor to give you a copy of the results and file them at home so you can follow your progress.
I have always been told and i have read on here as well as the Anemia section of the boards that the ferretin needs to be 70+ for a proper hair growth and shedding cycle.
My ferretin had slowly been dropping over a 6yr period and the doctor i was consulting at the time simply kept telling me that everything was ok with my results. Then i blamed the lauryl sulphates in shampoos and then blamed stress at work, but in the end i knew it had to be something serious. I never would have believed that my iron could be low as i am not a vegetarian and have a very healthy diet. In the end i consulted a new doctor about something entirely different and she organised an iron test and my ferretin was down at 8. It took me a good year to get it up to 25, then 29, then while on supplements it began dropping again so i opted for one iron injection per week over a 5 week period. This only got my figures up to 35. Now i'm back on the supplements along with some other iron tablets my specialist gave me.
It's not only your iron you want to get tested, but your B12, Zinc, vitamin D and even iodine and a proper thyroid test which includes TSH, T3, T4. My doctor tested a few other things too. I ended up being very low in the vitamin D and iodine and zinc was low but not extreme low. Your zinc needs to be correct for iodine absorbtion which in turn helps your thyroid. Your Vitamin D has something to do with the iron (cant remember it all now) and if your iron is low for too long then it too can affect the thyroid.
Hope this info helps and you can get a heap more help at the Anemia board