Hi Kelli,
The answer depends on your preferred restaurants. I would suggest going to the
Disney online reservation page and seeing if the restaurants that your family would enjoy are available. You'll also want to make sure that your preference of meal times have availability too. After all, you may want to dine at Chef Mickey's but you might not want to eat at 9:00 p.m. Another factor is your party size, if you are traveling as a couple, there may be tables for two. Larger families may have more difficulty getting last minute reservations.
Let me look quickly for you. For example, November 3rd dinner availability as of right now looks fairly booked up for reservations earlier than 7:00 p.m. There is a reservation here and there for earlier. Many popular places such as Crystal Palace, Chef Mickey's, California Grill, and 'Ohana are booked solid.
If you do some quick research at the link above, you'll quickly see if the Disney Dining Plan would be worth it for your family on such short notice for Advance Dining Reservations. You may want to try lunch reservations, out-of-the-way restaurants such as Olivia's Cafe at Old Key West and less popular meal times.
Best wishes to you! And enjoy a wonderful vacation!