I remember dog waste septic systems advertised years ago. A little search and I found them:Although I have never attempted to compost dog manure, evidently it is possible..
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I don't know if it worth your time or effort, but at least it is possible.
I only do cold composting in my chicken run composting system. So, dog manure would not work in there. Not a big deal as I don't have a dog. I do compost all my chicken manure and when I had rabbits, I used all the rabbit droppings as well.
https://www.the-compost-gardener.com/doggie-dooley.html
We always have dozens of plastic grocery bags available, so I just use one to pick up the waste, tie the bag, and toss it in the trash can.