Elf, I have just read your thread from start to finnish. The first thing that struck me was iron deficien aenemia. My son had this when he was just under two years. He would be slow to wake up, then be full of beans, and then slump and be sleepy for most of the day. No energy, not even at the playground. He was dark around the eyes, and bruised easily. Doctors in the uk did not want to do proper blood tests, as "they are so invasive and upsetting" for little children. He just zonked out while on holiday in Poland, and they had no qualms doing all the bloodtests, and he was admitted to hospital with seriously low blood count and depleted iron reserves.
Your dds diet sound a lot like my sons was. Cheese, youghurt, milk (all which inhibits iron absorption), chicken, fruit and veg. But he ate little. Iron deficient aenemia makes you lose your appetite. Most childrens multivitamins dont contain enough iron to build up reserves. They are only good if the iron reserves are already strong. It wont do her any harm, but it would help build up the reserves.
Changing her diet is surely not doing any harm, and worth a try. Could you try to limit the dairy, give orange juice with meals which contains iron (helps absorption), let her eat more red meat. Spaghetti bolognaise with beef, lamb kebabs, etc. Green leafy veg, such as spinach, bakes beans is good. Scrambled eggs where you use for example four yolks and just two of the whites. For snacks, raisins, dark chocolate, nuts, dried apricots. For fruits, berries, especially blackcurrants are high in iron and vitamin c, equally red currants sprinkled with some sugar if found too sour, blueberries are good overall and rasberries, too. This means you can make a berry compote for pudding, where you make sure to add black currants and redcurrants together with the other berries. Brown bread rather than white, peanut butter is ok if she likes it, as peanuts are high in iron.
Etc.
As my son did not agree with Ferrum, we had to go down the diet route in order to sort out his aenemia, together with a multivitamin which contained iron. It was hard to start with, but worth it when we saw that he started getting his energy levels back.
Like I said, even if she is not iron deficient, a dietary change wont harm her. Good luck.