Is it okay to go on a low-carb and high protein diet, with 1 hour of physical activity, to lose weight and be healthy?

Won't harm: Low carb, high protein diets are the basis of several diets such as atkin's diet. It is important to note that the key to weight is not losing weight but maintaining as close to ideal weight as possible over time. Significant changes in diet that can not be sustained over the years is likely to lead to a weight loss/weight gain roller coaster that is not conducive to good health.