Just ask them if you can bring your pet fish. They are going to allow you to bring your dog in the main compartment with you soon, they probably won't have a huge problem with a fish will they? make sure you ask though - read below story for one persons experience....
The day I smuggled my betta home!
Customs can be VERY funny with people transporting livestock and plants etc, I once went from America to Mexico and back to America.
We took a sort of picnic to have on the way there as it was a long Greyhound ride and amongst our food, we took a bag of apples. Well, neither of us ate any after we arrived, prefering to eat the local food (which was nasty) and so when we went home, I put all our possessions back in the bag, including packing another picnic to take back with us for the ride - including the same apples.
Well, the border guard on the US side arrested my apples.
I tried to tell him they were American apples, they had not been out of our room in the week we were there, they clearly were marked as American produce and they were in their original HEB bag. But he arrested my apples and threw them in the bin while we stood there. I felt like a horrible smuggler and an idiot, AND I was cross cos he took our apples off us.
Unless you make sure first, I wouldn't try it, it would suck to have picked a beautiful fish and then have to go bog-wash him because you weren't properly prepared. I'd contact the airline and get a letter saying you can travel with your fish.