I've been on a vegan diet for 5 years and I've never felt better. I get plenty of calories and I actually gained weight when I switched from a Paleo diet - that diet completely filled my liver with stones and I was not able to digest fat so I was super-skinny and felt horrible. Once your liver is clean, your body starts absorbing nutrients appropriately so you don't get hungry as often.
The diet that you mention actually sounds fine because there is little animal protein. The problem with animal protein is that it doesn't digest well and actually accumulates in your body as a waste product. However, I believe that if you eat a lot of vegetables on a regular basis, it won't hurt too much to eat some foods that aren't as good for you. The coconut oil, avocados, and other fats that you mention are great for you, although you may have some trouble digesting any fats if your liver is completely blocked up.
In order to be healthy, you really need to flush in addition to eating right. Once your liver is working properly, it will flush out the toxicity from your body and all your organs will begin working better.