I cremate. 1. Don't know the cause of death sometimes. Don't want to potentially harm any of the local animals, or my dog.
2. Its the "cleanest" and technically "safest" IMHO. And if I want to be burned when I die, I tend to not think its disrespectful. If they are your pets, you could have a little ceremony or celebration of life. I thank mine for their contribution to me while living, and bless them in the chicken afterlife

Hope that helps. You can always create a little chicken/livestock cremation area or do it in the fire pit. Your choice, depending on how ceremonial you want to get.
~cheers