Might not be your dog.
My dogs are large but would not hurt the bird on the nest - just nose under or move the bird. Only the most tenacious duck hides a nest in the sage brush and hatches here - most nest in the run or coop where the dogs are not allowed unless invited - they hang around the rundoor shamelessly but will not go in. They will even steal eggs from the wild birds but not hurt or try to catch the bird.
The only way an egg is safe around them is for it to be in the coop/run, in the house or hatched.
I know if they were allowed off the property (it is fully fenced so they do not roam) and should find a nest - the eggs would be history but the bird (duck, chicken, wild bird) would be safe and alive.