I shipped milk from TN to CA overnight when I was donating.
I used a standard styrofoam cooler that I bought at the supermarket. I used 5 lbs of dry ice. Put half the broken up dry ice in the bottom of the cooler and cover with newspaper, then put in the frozen bags of milk, then more newspaper, then the remainder of the dry ice. I'd then wrap the cooler with packing tape to close it. I'd take that to UPS and they'd put it inside a cardboard box and pad it and seal it and off it would go.
I don't know how that would work with fresh milk. I guess the dry ice would keep it cold, but I'd worry about it leaking and spilling.