Dr. Laurie Barclay gave a summary on Medscape. She lists a number of major points there. I'll excerpt the ones relating to dairy allergies and replacement foods.
• Food allergy should be considered in children with eczema in whom immediate symptoms developed after they ingest a certain food. Food allergy should also be considered in infants and young children in whom moderate or severe uncontrolled eczema persists despite optimum management, particularly if there is associated gut dysmotility (colic, vomiting, or changes in bowel habits) or failure to thrive.
• Bottle-fed infants younger than 6 months of age with moderate or severe eczema uncontrolled by optimal treatment with emollients and mild topical corticosteroids should undergo a 6- to 8-week trial of replacing cow's milk formula with an extensively hydrolyzed protein formula or amino acid formula.
• Children following a cow's milk–free diet for longer than 8 weeks, for whatever reason, should be referred for specialist dietary advice.
• Children with eczema and suspected cow's milk allergy should not be given diets based on unmodified proteins of other species' milk (eg, goat or sheep milk) or partially hydrolyzed formulas.
• With specialist dietary advice, children at least 6 months of age may be offered diets including soya protein.
• Women who are breast-feeding children with eczema should be counseled because it is not known whether changing the mother's diet may reduce the severity of eczema. If food allergy is strongly suspected, a trial of an allergen-specific exclusion diet in the mother may be attempted, with dietary supervision.