It is illegal to kill or damage native flora or fauna so penguin egg omelettes and albatross chicks are off the menu.
The introduced dandelions make a good salad, washed and then tossed in oil and vinegar with beetroot and walnuts. Shooting the reindeer is prohibited except under licence from the Commissioner, but he is not likely to grant one unless you have a good reason.
You can fish with a rod and line and may catch a marbled rock cod, or possibly one of the other Antarctic fishes in the bays. Only catch enough to eat - they are protected, and while nobody minds you catching the odd one or two, you'll need to buy an expensive licence to catch commercial quantities. If you pass a commercial fishing vessel at sea, it is worth swinging by to see if they offer you any, but be very careful not to get in the way of their fishing gear.