Yes. Avoid all milk and dairy products (including the hidden stuff--casein, lactose etc) in both your and her diet. When your daughter is at baseline (no eczema and healthy), you can try adding a pure dairy form (milk, yoghurt, or cheese) into your diet (or hers) to see if she reacts to it. Chances are she will react to milk, but some people can tolerate cultured dairy, but ALWAYS test. Eczema takes several days to a week to show up, so don't add anything except that one form of dairy for about a week. Also watch for things like excessive wetting, fussy behavior, night waking, eye circles etc. (Check out Doris Rapp's "Is this your child?" for lots of subtle allergy signs.)
If your daughter does not react then test another form of dairy until you know what she is able to tolerate and what she can't.
Many people who react to dairy can/do develop a sensitivity to soy, so I would consume it with caution (Well I wouldn't--DD's allergic to it :P) Think about increasing your consumption of nuts & seeds to get the calories an nutrition you have been from milk and soy. Hemp milk, sesame milk, cashew cream, coconut milk, almond milk are all great for cooking and adding to coffee/tea, and on cereal. With the exception of coconut milk they are easy to make if you have a blender and a tea towel. Also, you didn't mention fish--if that is a possibility, it's another great source for fats and vitamins.
Need more suggestions on food alternatives feel free to ask :D
R.