a few months after moving to this place we found out that the local pet cemetery is at the west fence line on my property, I couldn't make this up if I wanted to, well the walnut trees are doing real well there
I see no problem with burying dead animals under trees. I've done it plenty of times in the past.
From a permaculture point of view, you may not wish to bury chemically euthanized animals near food trees. Sodium pentobarbital is the primary drug used fur euthanasia, but others including various tranquilizers, ketamine, and others are frequently used. I'm not sure about the others, but sodium pentobarbital is rather persistent in the environment. In the past, I used to bury euthanize animals under pine trees. The trees grew absolutely great.
It's never too late to start! I retired to homestead on the slopes of Mauna Loa, an active volcano. I relate snippets of my endeavor on my blog : www.kaufarmer.blogspot.com