My dog will pluck them off of doves every time. She's ate a few quail heads from time to time. Never had any problems. I grabbed one out of her mouth when she was young. After just a few chomps she had pulverized it pretty good
Feeding the head in something for the dog. It's like a thank you for doing your job. But, you shouldn't have to do it. Just depends on what your relationship is like with your dog.
My personal opinion...It's a good way to start bad mouth habits, so I'd never do it.
We did it when I was a kid with all our bird dogs as a reward. Haven't done that much lately except with my new cocker pups. A dove head makes them sit at your feet looking up intently waiting for it or a command. Smart little dogs. Love them!