Well, since I have no way to know where in this huge World you are and therefore what CITES regulations (as implemented) in the Region /Country in which you reside.
Assuming that you are in North America, the regulations have been very slow on roll-out and there are tons of questions as to what and where information is required. The results is that although Breeders and Resellers are trying to figure out (mainly on their own), there is and will be tons of confusion during the coming year.
To my understanding of the information needed; the hatch date is very important. The Breeder needs to provide that on the Bill of Sale (strongly recommend that you keep that document forever) the Hatch Date, and the Sell Date (also known as a Resell Date). If you ever choice to rehome your Parrot, the Rehome Center or individual will need the original documents and a Bill Of Sale from you with the Sell Date.
Think of this as a like document trail as an Automobile!
When you set-up your appointment with your Certified Avian Vet (CAV) in the very near future, they will need a copy of the document set you have (complete with the Bill Of Sale). Commonly, Breeders and Resellers will require that you have your Parrot receive a 'New' Parrot Examination to maintain /support their Warranty. Your CAV, may elect to photograph your Parrot as part of their records (Strongly Recommended).
If you have a Mid to Large Parrot, I would strongly recommend that you have your Parrot Micro Chipped! This will provide a life long ID number for your Parrot that will support the Documentation Trail that you are beginning. It is also your only one of three ways of Identifying your Parrot as yours!
When traveling, keep a Document Set, including CAV medical document(s) and Micro Chip Certificate with you. Especially if you cross State Boards!
Unlike the EU, everything in North America is not yet in place! BUT, the laws are and therefore, if some Officer with to little to do, or more likely, you managed to Piss Them Off, - they can fine you, and if you are a real jerk, they can take your Parrot!!!