I also suggest repeat K3 or even P1 if you target DSS or Private School.
As u can try next year K3 as a small kid. At least both u and your kid can gain the experiences regardless the result. If u cannot get the offer , u can withdraw the lucky draw and repeat K3 again. If u can get an offer, or u can succeed via 自行派位, then no need to repeat.
Of course, if repeat is becoz of his ability not catching up with the others , then it's another issue.
You should not underestimate the difficulty of getting into a good DSS/private school. The number of applicants for the top notch schools have broken record this year and will only continue to go up in the next few years judging by the higher and higher birth figures.
So, "big" kids will have a natural advantage, when at such a young age.
My daughter is a big girl (not super one as she's Jan06). Yes, there is comparative advantage in applying those DSS/private schools. But it is not the only success formula as there are other factors that could affect the chance of success. I think you need to consider the risk of not getting a place in the increasingly competitive DSS/private schools after you repeat a year. Also, need to consider how your kid thinks as they will certainly not happy to repeat at K2/K3/P1 (I think repeating at K1 or PN really doesn't matter).
First, to see your children ability, comparing with other same age level classmates.
If she is behind, is there any other way to improve/help ? If no, you may consider to repeat.
If she is fine/superior, I don't think there is a need to repeat K2; unless you change to another kindergarten which is more difficult level and you want to go to those top famous DSS.
My niece is studying in primary school (normal). She is Nov small girl, she can get first 10 ranking in school every year from P2 to P4 now.