Hi Ray. How old are you?
I used to run 800 meters up to 3000 meters/two mile races. These are races where they are long enough that the body’s ability to use oxygen is very important, yet it is still fairly intense exercise. Stored glycogen in the body is an important fuel, here. On a ketogenic diet the body will have less stored glycogen, but I am not sure how much.
LeeAnn, above, is correct - training is very important, and the “long slow distance” where you are building your capacity to use oxygen and improving your cardiovascular system should be your main focus.
2 miles in 12 minutes - I think most of this would be done by a lot of training, whether you are eating carbohydrates or not. My guess is that a ketogenic diet, with the same level of training, is not going to make it easier, unless the body has enough stored glycogen (and that’s a thing I am not sure about).
Even if one is very well adapted to burning fat, it is still a slow process to make energy that way, and 6 minutes per mile is a fast pace, quite intensive exercise compared to how fast most of us can make energy from fat-burning. Again, my opinion, and if your proceed I will be very interested to see how you do.
Age group records for 3000 meters, converted to a time for 2 miles:
Men, 80 years: 13:12.
75 years: 12:04
70 years: 11:32
40 years: 8:20 