Slaughtered, obviously and in a cool box.
As long as you buy a ticket for it and have it treated like a pet (so pet carrier, have it travel in the hold with the other pets) I see little reason why not.
Of course dead pets might cause some raised eye brows with the pet handlers...
Well, you can't do it out of the United Kingdom:
We have precedence, where security in Cardiff airport confiscated a frozen turkey from luggage, as "perishable goods cannot be transported abroad without permission.".
Now this was for an international flight, but within the EU region, so I wouldn't be surprised if it applied domestically as well. However, as the article itself points out at the end, for unusual items like this, it's always best to call the airline in advance.