BISA and the shipping records are transcribed and compiled from other records and sadly often far from accurate so perhaps if we start again. Bear in mind that not all bdm's in South Australia were registered. All sorts of reasons including failure of the local registrations to reach Adelaide.
There was another John
WOOD with wife Elizabeth living in the eastern suburbs of Adelaide ie Kensington, Norwood and Magill. And another couple living south of Adelaide.
WOOD Alexander born 18 Feb 1840 at Adelaide, father WOOD John, mother GARSIDE
Elizabeth
Marriage - Stirling North is near Port Augusta.
WOOD Alexander 22 years Status not recorded Father John WOOD
WILSON Elizabeth 21 years Status not recorded Father William WILSON
18 Jun 1862
At the United Presbyterian Church Stirling [North] Fro 50/
Birth
WOOD Frederick born 25 Aug 1842 at Thebarton, father WOOD John, mother GARSIDE Elizabeth
Death
WOOD Frederick 14 years Status child Relative not recorded
6 Aug 1857
Residence Saddleworth Death Place Saddleworth Gil
F 7/91
Symbol
F Informant is a possible Family Member
Catherine born c1843 did not have her birth registered and she would be the youngest daughter.
AIKEN - On the 18th November, at Booleroo Centre Hospital, Catherine Thirza (Kate), loved wife of Hugh James Aiken, Booleroo Whim, and youngest daughter of the late John and B. Wood, Saddleworth, leaving four daughters and two sons, one on active service (reported missing).
Marriage
AIKEN Hugh James 24 years Status single Father Oliver AIKEN
WOOD Catherine 20 years Status single Father John WOOD
22 Apr 1873
At Holy Trinity Church Riverton Gil 95/232
Death
AIKEN Catherine Thirza 64 years Status Married Relative Hugh James AIKEN [Husband]
18 Nov 1917
Residence Booleroo Whim Death Place Booleroo Centre Fro H 414/368
Birth
WOOD Emma
18 Apr 1845
Father John WOOD Mother Elizabeth GARSIDE
At Reed Beds Ade 1/107
Death - and age is not quite accurate
WOOD Emma 70 years Status Single Relative John WOOD [Father]
10 Jan 1917
Residence Booleroo Whim Death Place Booleroo Whim Fro 407/399
Birth
WOOD Mary Jane
2 Oct 1847
Father John WOOD Mother Elizabeth GARSIDE
At Adelaide Ade 2/21
[Died before 1849]Birth
WOOD Mary Jane
18 Oct 1849
Father John WOOD Mother Elizabeth GARSIDE
At Gilbert Ade2/208
This is the Gilbert River Valley which includes Riverton, Saddleworth etc.Marriage
OTTAWAY Thomas Finch 31 years Status single Father Thomas Finch OTTAWAY
WOOD Mary Jane 28 years Status single Father John WOOD
9 Jan 1878
At Holy Trinity Church Riverton Gil 114/85
Hope that help sort out the children however none of this really helps with your request.
Cando