I don't believe there are any Wood Quail in captivity in the USA. I think there are some in Europe in captivity but I may be thinking of Rain Quail. Importation of even captive birds is a tough and expensive proposition.
I found another regulation that said that you must be out of country for at least one year before inporting your pet bird so much for a 4 month vacation. Although that's pet cant get strate answer on livestock. As for eggs you have the same problems one year and own the parents for 3 months prier to applying for permits
Every time I'v ever been to Mexico, I'v been tempted to stuff a Macaw under my shirt tail and try to walk normally back across the boarder. These days I'd guess it would be a stiffer penalty for get'n caught with birds than a big bag of contraband!