I never heard of the anemia, but I've also never been in your situation.
I hardly think your daughter will "starve". I would offer her up some simple solids first, before you even show her a sippy cup. Start with things like applesauce, warm carrots, etc.
I do agree that ANY child can "fill up" on milk/formula and have a harder time taking solids.
Our little guy loves nursing (never took to formula). I am in the process of weaning him and he isn't happy. The OB said, "You just have to be tougher than him."
Think of it this way. No matter what, you KNOW as a Mommy that your daughter can't stay on formula until she's 5 right? So start transitioning. Don't "give in" because you know in your mind she needs to move on.
It sounds like this "will be an issue" since she likes her formula so much. So keep the bottles/sippy cups out of sight and offer her FOOD. You can also try adding a small amount of chocolate/strawberry powder to her milk or go for soy milk. It is a different taste, so she will have to get used to the "new" milk. You might try mixing her soy formula powder with her milk so that it tastes like her soy and slowly "wean" her off the powder added.
Milk can be constipating, so I'd hold off on bananas and other foods that may bind her up while you are transitioning. Stick with apple sauce, yogurts, pureed veggies and simple finger foods.
Best wishes