I am not seeing any good reason to take higher dose. If you have any acute deficiency of Zinc, then you can opt on guidance of your Doc. For improving immune system you can have different types of Vitamins and Minerals such as Vitamin A, Vitamin C, Vitamin E, Vitamin D, Selenium, Zinc. Some herbs like Turmeric, Ashwagandha, Amla, Tulsi, Giloy, Black Pepper are also beneficial to improve immune system. Even one teaspoon of Honey regularly is beneficial. Regular exercise is also good for immune system. In My opinion you can opt for any high quality multivitamin and most of them are with variety of Vitamins and Minerals.

I don't recommend zinconia tablet as it is for infections in the body