We love our pets and it's hard to say goodbye especially for a child.
With our cat, Sunny, he insisted on going outside although he appeared injured, thing is--he never came back. We suspect he may have gone to a special place to lay down--forever.
We miss him so much, but we also know it's better that he wasn't suffering.
The main thing is to help your child by talking about the loss and listening to their own ideas and understanding of death. It's important not to dismiss their feelings while grieving or to belittle their pain by careless statements. This can be used as a learning oppurtunity and a chance to connect as a family. Don't be afraid to let you child know you are feeling sad as well. Remember that anger can also be part of grieving.
The Aspca has a lot of good tips on pet care. You can even get tips on your mobile phone.