Two years ago my friend's small kid (born in end of Dec) got admitted to HKUGAPS
(http://www.hkugaps.edu.hk/zh_hk/). If the kid performs favourably during the interviews of ANY school, I believe it won't be a big problem.
I also know a friend who's kid was born in Sep/Oct (currently a K3 student). But unfortunately the kid got no offers despite having tried quite a no. of DSS/private schools. The parents have decided to let their kid repeat one year and then try again in the coming year.
I think it really depends on the performance of the kid.
My girl (born in late Sep) is accepted by HKUGA this year.
However, my friend (boy, born in May) tried 11 schools, but all fail.