Hi. Transit visa of HK for 1 day

Dear sir. I am a Pakistani citizen and moving to New Zealand for PhD studies. I have valid NZ entry permit and I am taking Cathay Pacific flight to NZ which puts through HK. I want to apply for HK Transit entry permit so that while going to NZ I can stay and visit HK and obviously learn something or see something new. Do I need to apply to HK immigration Dept in HK or I can get the entry permit from Chinese Consulate in Pakistan. How long would it take for the application to be granted. I will be grateful for the response.