Two parts to this.
You must have either your AP or a voucher in hand to order the DDE card.
You do not want to order it until a few weeks before you start your vacation. The DDE does not tie its effective period to the AP but to the date of ordering the DDE card. Normally if you order it by the 7th of a month it will be good through the last day of the same month the next year; however, if you order it after that date it will be good to the last day of the following mointh the next year. (Example order today good through 11/30/07 but order next week good througH 12/31/07.)
In your situation you would probably not want to order it until May 8 or 9, and it will be good through June 30, 2008. If you do not receive the card before you leave home, you could call the DDE office (8:30-4:00 M-F) and they will have a temporary card waiting for you at the Guest Relations Office outside Epcot's Main Entrance.