I was introduced to this phrase by some Australian friends - whenever they had a 'barby' they told everyone to bring a plate - which they did, loaded with all sorts of barby fare - steaks, prawns, sausages, burgers, chops, and so on. When I was out there it was a general term whenever anyone was having a barbecue. So, I reckon it came from Australia.
I understand that this is an expression used in Australia and New Zealand, the equivalent of "bring a basket supper". Don't know where it originated. An unfortunate friend of mine actually took an empty plate to a party.