A good friend of mine from playgroup found out her son had about the same iron levels about 6 months ago. She suspects he has coeliac disease. It's not confirmed as she said the test requires more food eliminations and blood tests- both of which he's had lots of lately so she's holding off for now. But she has put him on a gluten free diet and he's improved amazingly. She didn't want to use supplements (I'm not really sure why) so mostly she boosted his iron with organic livers and it worked really well.
Must be such a relief to have an answer and know you can help your daughter feel better now