Rather than just tell her to take iron. As she doesn't have heavy periods, has a decent diet with plenty of meat, doesn't drink tea or milk (so less chance of iron absorption being reduced). She does have coeliac disease but has been on a gluten free diet for 10 years now. Surely they should try to figure out the cause as there doesn't seem to be the usual obvious causes.
Obviously going to get her on iron, and increase iron foods more (pate on toast for breakfast instead of cheese on toast etc.)