The last question is the easiest. St George the Martyr is a parish in London (since at the time London was actually only the square mile Middlesex officially) in the Holborn area of London. If you check the IGI you find
MARY ANN COX
Birth: 26 JUN 1814 Keppell Street Russell Square Baptist, Holborn,
Father: JOHN WILLIAMS COX
Mother: CHARLOTTE
CHARLOTTE COX
Birth: 18 JAN 1816 Keppell Street Russell Square Baptist, Holborn,
Father: JOHN WILLIAMS COX
Mother: CHARLOTTE
JANE COX
Birth: 11 SEP 1818 Keppell Street Russell Square Baptist, Holborn,
Father: JOHN WILLIAMS COX
Mother: CHARLOTTE
SUSANNAH COX
Birth: 09 AUG 1820 Keppell Street Russell Square Baptist, Holborn,
Father: JOHN WILLIAMS COX Mother: CHARLOTTE
JOHN COX
Birth: 19 JUL 1823 Keppell Street Russell Square Baptist, Holborn,
Father: JOHN WILLIAMS COX
Mother: CHARLOTTE
ELIZA COX
Birth: 20 DEC 1825 Keppell Street Russell Square Baptist, Holborn,
Father: JOHN WILLIAMS COX
Mother: CHARLOTTE
For John Williams Cox and his siblings you need to search St Mary's Harrow on the Hill Middlesex baptisms. The registers are at the London Metropolitan Records Office. I think only the earlier registers have been indexed.
There is this potential marriage on the IGI
JOHN COX
Spouse: ANN WILLIAMS
Marriage: 17 OCT 1791 Saint James, Paddington, London, England
People did come into London to marry and then return to their own parishes
I presume you can find Charlotte's maiden name from an Australian death certificate of one of her three children who emigrated? If one or more of her three older daughters survived she may well have chosen to remain in England with them. I would think your main hope of finding her is to wait until there is a computerised country wide index of the 1851 and 1841 censuses and search that in the hope of finding a potential Charlotte Cox living with one of her daughters. The Ancestry website now holds censuses indexed 1861-1901. They will be working on 1851 at present. Nothing shows for a potential Charlotte in 1861.
Regards
Valda