There is a huge difference between organic and commercially raised dairy cows, and there is a huge difference between what the milk is like for humans, especially small humans. Organic milk means that the cow has been raised with no antibiotics, no artificial hormones, and no petrochemicals in it's feed-pesticides, fungicides, herbicides, fertilizers, etc. Usually organic also means primarily grass fed cows--which are much healthier.
Since all the toxins that ARE present in non-organic dairy and are NOT present in organic dairy are fat soluble, these toxins will build up in the body, being released over time as the body fat gets utilized.
Among other things, among my three daughters, who had primarily organic dairy (and not lots of that, either), they did NOT develop puberty early, while about half their classmates (the ones who ate lots of fast food, lots of dairy from non-organic sources, a very "conventional American diet") were getting their first periods, bras, acted like pre-teens and were about a foot taller than the other girls (the ones with the organic diets) by 9-10 years old. The others, including my daughters, had more normal development around 11-12 or even later.
It's pretty scary, especially in this day and age when so many women end up with breast or other cancers--again, likely from fat-soluble toxins stored in fat dense tissues. I would stick with organic dairy, and I would consider just keeping the dairy levels down altogether, since it is not an essential food.