Genia,
My older son worked with me when I helped out at the shelter; he was 8 or 9 at the time. I never tried to pull any punches with him so he always knew that some of the animals would be put to sleep. This gave me an opportunity to explain all the reasons why being a responsible pet owner was extremely important and what the responsibilites of a good pet owner are. It was a very hard lesson to learn, but I am proud that he loves animals and understands what it means to care for a pet over the course of its life.

Whether or not your child can handle understanding depends on the child's level of maturity and how much real life they've already been exposed to. My younger son was helping trap kittens at age 10, my older son started helping me load vaccines at age 11. They are 11 and 18 now.