There is no provision in the immigration rules for a minor PBS dependant to apply for settlement separately from the PBS migrant that he is dependant of (
319J).
Once you are granted settlement there will be no need for the (UK born) child to apply for settlement as the child will entitled to register as a British citizen.
That said, if your settlement application is refused for some reason then the child will become an overstayer if a valid application for leave to remain is not submitted before 04-Nov. If you suspect that this may happen (your settlement may be refused) then the best option is that the child applies for extension of PBS dependant leave before his current leave expires.