Anything is possible and people's plans do change. However, the first two weeks of December are among the most difficult times for
DVC members to reserve if they cannot/do not use the 11 month window. Those two weeks for 2002 have had waitlists even before the 7 month window opened. To get a studio at any of the DVC resorts now (or later) for all of the days you want will be very difficult, but it could happen. Maybe you will be lucky!
My advice is to make a back up reservation somewhere in the World for cash now, assuming that you are going at that time even if you can't stay at a DVC resort on points. Get a room only and make sure you can cancel it without penalty ahead of time. I believe the current policy is more than 5 days before arrival to avoid a penalty. Then as soon as you are able, call for a DVC reservation. Get on the waitlist for any days you cannot book.
Another option is to use points to stay at one of the non-DVC Disney Hotels. Do keep in mind, though, that once you book a non-DVC reservation, you cannot cancel it to use the points at a DVC resort. There are other things to know about staying at a non-DVC WDW resort using points, so if that option interests you, be sure to ask for all the "rules/things to know" before you book.
Good luck! Hope we can welcome you home, soon!