Dealing with the death of a pet is definitely a non-trivial event. Often a pet has lived with you for many years. In a lot of cases, the pet will have been with you longer that a child or a spouse. It's not surprising that a pet's death can affect us so profoundly.
Unfortunately, it's easy to dismiss the loss... "It was only a cat..."
More and more places are acknowledging that this loss can be extremely traumatic. Here are some sites that deal with the topic:
Humane Society - Coping with the death of your pet
ASPCA Pet Loss FAQs
ASPCA - Ask the Expert about Pet Loss
Euthanasia and death of a pet
Explaining pet death to children
Ten tips on coping with pet loss
PBS Kids: Dealing with death - pet loss
ASPCA - Helping your child when the family pet dies
The library has an excellent selection of books for adults and children on the topic.