@tsarstepan,
In Pa alone, we have about 1 million hunting licenses and about 350K hunters go for doves. I only hunt rabbit and wild goose so I don't see the need to hunt stuff like doves, quail, gallinules, rails, or some of the small ducks like buffleheads (Who are just too cute to shoot and eat).
Usually the rule is"you hunt it, you eat it" and 350K dove hunters for 2 months of banging away in the corn still doesn't come close to denting the population. In delawaer and Maryland (especially the Eastern shore), dove hunting is a prelude to the big season of waterfowl slaughter.
Look at what happened to the passenger pigeon.
Heres a quail stuffed with venison sausage, To be completed it should be served with a tart cranberry/ lingonberry sauce
Yeh ceilli is correct that most restaurants will call all this stuff squab , but in really high end ones they call a dove an a quail a dove or a quail because of the taste preferences of diners.