Hi, I had this.... my ferritin was around 13 so also much too low. Iron did help and my hair grew back, although it does take a while to notice a difference and for your ferritin levels to pick up.
I find it really strange that GPs don't seem to know about this. I also had to wait months, tried all sorts of products bought off the internet until I found a website one day saying about the link between anaemia and hair loss. The GP had tested for anaemia, but the article said to test for ferritin levels. So I went back, and was referred to a trichologist who suggested a ferritin test, she said they usually only test haemoglobin levels which, even though it might be in the low normal range, does not always show how low your iron levels really are. I struggle with oral iron intake, as it makes me really constipated but I've found spatone to cause me less problems. You have to take vit C with iron otherwise it doesn't get absorbed very well, and also avoid tea for about an hour before and after taking the iron.
All the best to your wife, at least now she knows what is wrong and chances are her hair will all grow back