I agree that one should stay away from refined carbs, but not simple carbs in whole foods. Fruit has simple carbs, but if you avoid fruit, you will be avoiding a lot of fiber, and micronutrients.
What is your reasoning for going low carb and high protein? Are you trying to lose weight without working out? If so, you will have a nice looking body with an unhealthy engine. You should work out to maintain muscle mass and improve cardiorespiratory health. If you workout moderately, you don't need much protein at all to maintain muscle mass. Less than 10% of total calories. If you are working out very intensely, you might need up to 20% protein to build muscle mass. There are plenty of vegan bodybuilders consuming around 20% protein.
All that said, if must do a high protein diet, then a plant-based diet is best. You eliminate the cholesterol and a great deal of saturated fat. Plus, the protein in plants doesn't leach calcium from the bones.
If you want to lose more weight, eat whole foods and work out at a higher intensity.