As someone who has recently gone through (is still going through) the loss of a loved pet, this list from Angela Hartlin on the unique aspects of grieving for a pet is extremely accurate.
My only wish is that the headline was more about how pet loss is "different" from human loss instead of "worse." Loss of any sort hurts. We don't need to make it worse by creating a competition out of it. Grief is grief. Be kind to yourself. And others.