You can, but whether it's worth it to you is the question.
Presumably the tickets you bought were for the full time you plan to be at WDW. To get DDP, you have to buy a minimum of a two-day base ticket for each member of your party and stay at a Disney resort. If you plan on returning to WDW at some time in the future, you can use those two-day base tickets on that future trip [but you'll have paid $172.53 for each adult and $156.50 for each child 3-9] to upgrade to whatever you need for tickets. You won't be able to have DDP on the second trip unless you buy more tickets then...
If you don't plan on returning, that investment is pretty high for your trip.
You should look closely at what you expect your costs for food to be versus the added cost of extra tickets. I'm guessing the discounted Military tickets are worth more to you savings-wise than getting DDP.
EDIT: If the above poster is correct and you don't need to buy base tickets as well, then I stand corrected... I wasn't aware that was possible....