I know guys just north of the Mexican border in eastern California who used their VHDs for doves, until one keeled over dead.
These were excellent breeders and trainers of dogs with field prizes, who knew how to care for dogs, cleared their mouths of dove feathers regularly, etc. The little feathers get deep into their throats, though, and clog things up where you can't get them out in the field.
Don't know what it's like where you dove hunt, but a mouthful of feathers keeps a dog from being able to pant, and a dog who can't pant when it's 115 degrees in the shade, is soon a dead dog.
Now if you're using a dog to retrieve them from canals, that might be okay, but I still wouldn't risk it.
As for me, I like to shoot doves more than I like to eat 'em anyway. If one gets stuck way deep in the brush, there are some other animals who will make good use of the meat. I'm not killing my dog to get another dove.