This has come up before IIRC, but if you are running beagles who like to chase pheasants... I think the standard answer at the time was that 'to be safe' you should have the stamp, but I don't particularly like that answer. I have no interest in shooting the birds so I don't see why I should have to have the stamp. I only ask because the above answer mentions attempting to flush pheasants.
A bad day hunting rabbits beats a good day of anything else!