Hi Carol,
A ship leaving London 20th Dec. 1912 would have arrived in Sydney in early Feb.1913. The Georgina Dixon on board the "Gothic" was only aged 20 and her husband was Thomas, not Henry. (UK outward passenger lists on Ancestry.co.uk.)

Your record looks like an Ancestry.com index mistranscription of her husband's forename, and her age not given on arrival? Are you able to look at the original record?

Also, if the US 1890 census isn't available, can they be found on the 1900 one?

Sue