I have to agree with Sandman here. The suffering and death of an animal really does matter, both to the animal itself and to those that love it (whether humans or other animals).

So yes, a comedy song about an animal suffering and dying belittles the value of that animal and of its suffering. The argument that an animal is less important than, say, a child, and so it's okay to laugh at the animal song, is spurious; suffering is still suffering.

As has been said before, though, we all have our different opinions. Some of my good friends find songs about animal suffering amusing. But I don't; and I find it hard to understand why others do.