In general, guests wishing to purchase DDP must buy a package reservation including a room and at least 1 day park tickets for everyone in the party age 3 or over.
There are a couple of exceptions. Annual passholders and those eligible for the military room discount may purchase ticketless packages. DVC members booking through Member Services may add DDP to their reservations (DVC does not book packages).
If you don't fall into any of these categories, you must purchase at least one-day tickets as part of a package through Disney to add a dining plan.
You can check into whether you would have access to any discounts if you book your package through the AAA
travel agent. Or you could look into renting DVC points, that is not a package and you may buy tickets separately. However, there are some caveats to renting points, the biggest one generally being that it is difficult to cancel the arrangement.