I had a live duck in a show, which really isn't similar at all to what you're describing. It was not very friendly, and I was the one in charge of bringing it to the stage every day. The other crew knew I was coming as he loudly quacked his way down the hallway on our arrival. He had his own (dry) baby pool it knew was his offstage, and loved that. We had a water-filled moat onstage, and prior to being filled, he would jump in it every time (which was not the plan). We got worried what would happen when we put blue-tinted water in it - would we end up with a blue-tinted duck? - but he actually avoided that water like the plague once it was in.
He did get loose one time while I was retrieving him (he was not supposed to be able to fly, but we'd had him around long enough his feathers had gotten longer or something), and headed towards ours cabaret/dining space. In hindsight, I really wish I had caught him while yelling out, "You! Back to the kitchen!" That said, I was incredibly afraid he was going to fly into the glass windows and break his neck. We had no backup duck - though he was only used in a prologue and probably could've been adjusted. In fact, somehow the original (new) script had called for a pig and we had it changed to a duck at some point.....don't ask me.
Totally separate, my husband the stagehand had an incredibly lovable pet duck as a child. It even took trips to the A&W root beer stand with them and got his own snacks. We have two photos on our shelf...me with the psycho duck and him with his childhood pal. Makes me smile every time.