All dairy can lower iron if a child is consuming too much. Limit the dairy to 2 servings a day. 1 serving is 8oz milk, 1 oz cheese, 8oz yogurt.
The only way to increase iron is to eat it or take an iron supplement. Increaseing oils won't help because they don't contain iron. Your doctor probably feels 10.7 isn't low enough to use a vitamin and that increasing iron rich foods should do it.
Iron rich foods: all meats (chicken, fish, beef, pork, goat, deer, lamd, any kind of animal), beans, eggs, iron fortified cereal, dark green veggies (spinach, brocoli), prune juice
The iron from meats (heme-iron) is the kind your body obsorbs best, but many young children have a hard time eating them. Offering a vitamin-C food with the iron food helps increase obsorbtion (split pea soup w/ham, tomatoe based chili w/beans, dry cereal w/berries).