Take your child to a local animal shelter.

 

Say that you're considering adopting and ask what you can donate (money, pet food, etc.).

Take your child to visit the animals.

If your child is so inclined, he can volunteer there.

One thing to watch out for is that your child's empathy stems from his longing for sympathy FROM others.

There're cognitive and affective empathies. It'd be interesting to watch what your child has.