Certified GKH Gardening Expert
No, it is not a good idea to use this in compost. About 95% of the time, manure from animals, like dogs, will not cause harm - but you shouldn't use it in the garden because of that other 5%. Meat-eating animals can carry harmful bateria that may pose a threat to both plant and people (when used on veggies).
I throw it in a compost tumbler with the shredded leaves and grass. I have only used that mix for the flower beds however and they seem quite happy with it.