This doesn't sound like a healthy plan to me. Your brain requires glucose to function. When we eat, glucose is preferentially obtained through carbs then through a process called gluconeogenesis by breaking down protein. On VLC diets, fatty acids are converted to ketone bodies that can provide energy to the brain, but even bodies adapted to a VLC diet can only get about half the energy required from ketones. While fasting for a day or two, a normally healthy person's body does a good job of maintaining serum (blood) glucose levels (which is how the glucose reaches your brain) by releasing glycogen stored from the liver. After that it resorts to breaking down its own protein (muscle) and at that point it is called starvation.
So, if you were to fast for two weeks, after the first few days you would be breaking down muscle (not-so-fun-fact: people who die from starvation often die from diaphragm failure due to autophagy of that muscle). So, I do not think this is healthy and is unlikely to help you meet your goal of feeling more energetic.
Here's a good resource that talks about blood glucose levels and fasting/starvation (though I think it should cover "rabbit starvation" more thoroughly with a reference to the need for fats):
http://www.medbio.info/horn/time%203-4/homeostasis1.htm The relevant section is "Glucose Production in Starvation."