The animal is the owner's property. He can do what he wants. What if the owner wanted to crash his car against a brick wall so that no one else can be hurt? A narco-libertarian would support his right to do so. The animal is also his property so no different.
What about children? Children in common law are property of their parents. So the narco libertarian position ought to be that whatever the parent wants to do is fine. Unless they want to say that children are in fact people with all the attendent rights. In which case they would have to support children suing parents for not giving them ice cream and the like.
There is no end to the absurdities inherent in the narco-libertarian world view when properly explored.
Except you aren't properly exploring them. How can you claim to do so when you have to resort to made up terms to support your position?