Terry
Just to get a 'fix' on birth registrations around that time, we recently extracted the birth notices (and death notices for children under 5 years) for 1871 in a major NZ newspaper. Some 27% of births were NOT registered - the requirement was to be registered by 60 days after birth.
Some died before the 60 days so the death was registered but not the birth, some who died had neither registered, and a small percentage (who did appear to live)did not have the birth registered. For some parents the fine incurred for late birth registration was the barrier, for others (ex nuptial particularly) then social stigma was probably the barrier.
Elli