The term ‘milk baby’ refers to babies and toddlers who suffer from iron deficiency anemia (IDA) as a result of drinking too much milk. A baby or toddler that consumes more than 2-3 cups (16-24oz) of milk daily can be considered excessive. Generally, it's when they are consuming a litre of milk or more every day (yes, it happens) and thus they can head down a very quick path to IDA.