How to teach a child to respect animals?

At 2 years old, she is too young to understand. I would teach her through example with stuffed animals. Stroking a stuffed animal and treating that toy with gentleness. Perhaps, that will help her to learn to be gentle to animals. But it sounds like she just needs to play and get all her energy out. I would wait until she is about 4-5 years before really teaching her about how to be gentle with animals.