I have two sweet girls and they BOTH did the same things when they were younger. I don't know why kids do this but my kids grew out of it and are animal lovers. I'm NOT saying it's OK for kids to harm animals (calm down PETA :)
My 4 year old still chases around the dog, she thinks it's funny but I can tell the dog doesn't like it. Its embarrassing but she did hit the dog when she was younger (not hard but still). My oldest daughter used to chase the dog around with a toy shopping cart, dog hated it. Bottom line, its entertainment for them and it's like a living toy to them at that age.
I am sure you are a great mom, but my child did it when she was a little bored of her toys and was waiting for me, for dinner, for something.
You need to treat it like any unacceptable behavior and discipline her with a time out. Yes, I have spanked my child but I think spanking a child to prevent them from possibly hitting an animal might be sending an oxymoron message. Just a thought.