My DS was diagnosed with low iron in January (about 7mths old) after we had blood tests because of a persistent cough and cold thing. His levels were down around 4. All we had to do was give him some liquid iron supplement. DH (who took DS for the results of the tests) was told by the chemist that sometimes the children don't like the taste of the iron stuff and that it could be washed down with a bit of juice if needed. DS takes his straight from the syringe that we use. We were told to get another BT after 2 months to see what his levels were like then. His levels have improved to be in the low end of normal (at 9 months) so we were told by the GP to keep up giving it to him for another month and then we could stop with the supplement.
Hopefully that's all it will take for your DD to improve her levels. We also made sure we tried to give DS meat a few times a week at home for dinner (wasn't always awake) - he tends to get some during the week at CC already.