I'm a reptile keeper and don't know much about how they handle birds but strictly speaking you will probably need at least a CITES export permit when you leave the USA. You need to find out of your parrot is appendix one or appendix two.. Appendix two is easier than one. With appendix one species, you need two pemits. One from the country of origin, and one from the importing country. You should check with US fish and wildlife, and find out just exactly how they handle pet birds. Unless they have a special provision for one of pets, it could be quite a hassle, especially if your bird is appendix one, with no proof of legal origin.