Katy will be bringing that dog as a companion during the US part of the tour. Full stop. There will be no dog on stage as that would be animal torture, and most likely impossible to insert a "dog part" in a fully rehearsed show that does not include a dog for 3/4 of the world tour.
I was at a concert tonight that had 2 dogs on stage (Colbie Caillat, Malibu Sessions Tour). I enjoyed the concert a lot and the dogs seemed to enjoy it. So those of you who basically accused me of animal abuse for thinking that Katy would have Butters on stage owe me an apology).