The CMs at the DDE line can give you a pretty good idea how long it will take for you to receive your card -- seems to me it took about 3 weeks, but that was several years ago.
However, you don't really need your card before you go. You can order it anytime (even on arrival), but remember that the DDE office is only open Mon-Fri. If you're not going to receive your card in time, they can arrange for a temporary card to be waiting for you at the Epcot Guest Services office (which, of course, is open 7 days a week).
Unlike every other Disney thing I know about, DDE does
not activate the first time you use it -- nor does the activation start when you order it. It starts when they
manufacture the card.

Makes sense to someone, I guess.
The card is good for 13 months, and the CMs can tell you exactly when your card will expire when you call to order. They told me to call back a few days later because doing so would result in the card lasting an extra month and allow us to get three trips on the same card.