Check Overseas Births Register for army births?
Source Gro Regimental Birth Indices (1761 To 1924)
Archive reference REG1
Record set British Armed Forces And Overseas Births And Baptisms
First name(s) John
Sex Male
Last name Burke
Birth year 1828
Regiment 74th Foot
Type Armed Forces
Country Ireland
Place Cork
Page 44
Archive
General Register Office
Record's year range 1828
Volume 1304
Line number 102
Category Birth, Marriage & Death (Parish Registers)
Subcategory Civil Births
Collections from Great Britain, UK Other
There's another one with the same details, but on page 48 instead of 44. Used findmypast for that, not sure if that's the best one to use for these records? Too bad John Burke is such a common name, it's hard to figure out who is who. This one would've been 30 when Eileen was born.
No St Aubyn Burke, Stella Burke, Eileen Gertrude Burke on any of the New South Wales BDM, newspapers, findmypast, familysearch or ancestry. Couldn't find any more information on Eileen from Paper's Past either (NZ newspapers), only two obituaries which Christine53 found.
Tried NSW BDM for just Burke and parents given names as John and Stella, no records.
Waiting on NZ death certificate. Going to continue with Australia in the hopes of finding something. Tried Victoria and QLD too. If I'm unable to find anything will post to the Australian subforum.