Henry came up with a few symbolic accessories for his cars even though Ford didn't make them. The quail came before the greyhound but the greyhound lasted longer in the V8 era.
Quail and the larger pheasant are from the same family of ground nesting birds that are common to North America in the form that Henry knew. There are other species of the same family all over the world but there are a lot of differences depending on location. Hunting them is still a seasonal activity for those that love to hunt game birds. Ground nesting birds don't fly much farther than they have to to survive but they get there pretty fast. Even the wild turkey, still active in this part of the world, flies very fast for a speedy getaway from predators.