Well you know how nitpicky airplanes can be (for very good reason). Doesn't matter if the water is safe for the fish, there may be ... something in the water that we can ... make something out of. Like, just because it's safe for a fish doesn't mean we still can't do something with it. Always be doubtful and pessimistic when it comes to danger in flying airplanes and whatnot (safety first!). I honestly would understand if they don't allow fish on cabins hundreds of years from now.
But, another +1 on shipping to your mom's house. Hopefully they'll be okay! Research extensively on shipping ...