What would you be cooperating to do?
-set standards that all members abide by, potentially bypassing "tragedy of the commons'-style coordination problems
-share information which, in a more cutthroat environment, would be considered "trade secrets".
Not sure how these would apply to the dairy industry specifically; it just seems overly broad to say that price fixing is the only plausible form of cooperation.
The only things an economic organization can do are raise prices and lower costs. For a labor union, costs are labor; from the consumer end the workers' "lower costs" mean less work is being done, which shows up as higher prices for consumers.