It should be dairy milk. Dairy itself means dairy farm and dairy products.

Dairy can also be used as an adjective. dairy milk looks like milk from a dairy.

There are many online dictionaries, including Kingsoft and Baidu dictionaries.

This is my interpretation of Kingsoft PowerWord 2007:

Dairy farm, dairy farm, shop selling milk, cream, eggs, etc., dairy products

1.of milk; Made of milk; Dairy 2. Dairy industry; Dairy producer

dairy cattle

Cows (collectively)

dairy maid

Dairywoman

dairy man

Dairy owner; Dairyman; Dairy merchant

dairy products

dairy produce