Fun story: 2 years ago, my brother and I went through LAX on my way home with 2 koi roughly 2 feet each (separate bags). When we arrived, I politely told one agent, they had me walk to the side and they'd get their supervisor to come. The supervisor simply had me take everything out the suitcase (clothes, computer, etc), took a look of it all, inspected the living fish, opened the bag, took a sample of my water, tested it, and it all checked out. Went through 30 minutes later.
It is up to TSA and the airline if they allow it. It was a sight to see, people were staring, I was laughing, the agents were laughing, some were even jealous how gorgeous the koi were. One told me usually its tiny fish like a rare beta that people transit, never a 2ft koi. If you check TSA's website and/or calling them directly, its up to the agent. Doesn't matter the amount of water in the bag as they'll inspect the "living specimen" and sample it to make sure its not something like alcohol.
Most of the time though, you never have to inform the airline.
