You seem very certain of Eliza's birth date - the last quarter of 1863. If you don't have any official certificate, but are relying on census information, there may be the possibility or error.

Many Elizas were in fact Elizabeth and vice versa - they just love to make life difficult for us - and there are a number of Elizabeth Smiths, as well as Eliza Smiths (with a middle name) where the birth is registered in Portsea RD at around that time.
There are two possible brides for James Henry Hansler in 1883 - Eliza Smith and Eliza Ann Thomas. Have you established that it was definitely Eliza Smith who married James Hansler? From a birth certificate of one of the children perhaps, since you don't have the marriage certificate?
An Eliza Ann Thomas was born in Portsea RD in the June qtr of 1862.
I too think that the marriage certificate is the best option on this one.
Nell