I would like to visit Hong Kong during my holidays next month.

Yes, you need to apply for a HK. Luckily, it is easy to get one in Beijing. Go to the Office of the Government of the HK Special Administrative Region (HKSAR) of PRC for an easy access. Its location is no. 71, Di'anmen West Street, Xicheng District. Their email address is as follows for your reference:
bjohksarbjo-hksarg.org.cn