The biggest difference between a '64 and a '65 is that the '65 is the first year with axles forged with their flange as one piece...
There are a number of options for replacing the original drum brakes, however. First you need to cut the swaging of the wheel lugs, these retain the drums on the axle and prevent servicing the brakes without removing the tapered hub from the axle shaft.
Once you have done this you get new lugs and drums of the later style. Finned drums to go straight over the 10" x 2.5" brakes you have are available on and for 2WD Dakotas. 11" x 2'5" drums can be had if you get the whole assembly from various models from '65 on, probably easiest to find on pickups.Again, there are finned versions of these drums and they aren't expensive buying them new.
Fitting the new backing plates will require that you break the grip of the taper on the axles, clean the components again and refit them as part of the assembly operation. I have read on a few forums that all you need to do to break the taper is loosen the big nut slightly (not even a full turn), drive gently around the block and it will come off. Others may know better, and, of course, there are pullers you can buy, make or hire.
As you do all of this it gives you a good opportunity to swap out the left-hand thread lugs on the back, and if you do that you probably should change the front lugs as well. And if you're fitting the bigger brakes to the back it won't hurt to fit bigger brakes to the front, others here will know better than I do what models have the 11" x 3" drums, they're not hard to find at wrecking yards and I don't know of any reason whole assemblies (backing plates to drums) can't be retrofitted to your model. They were, in fact, an option for 'police and taxi' use in the '64s.