I have carried fish onto planes (for internal flights, not international of course) a number of times (in cooler bags), and given them to others to do the same, with no problems. You just don't say "Oh, by the way, I have live fish in my bag"
I travelled with an axolotl in an ice cream container once. The air hostess (remember when all flights had them?) said "Eeewww!" but didn't say I couldn't carry it.