Do you have Ann's death certificate - does it say if she was a widow or married? Who was the informant?
Have you checked her burial plot details with Ballarat cemetery to see if her husband is buried with her?
I checked deaths in Victoria without finding him
NSW are free online so you can have a look yourself.
Where was he born? and where did they say that they married? as an English marriage would give his father's name and occupation. The parents given at death are only as good as the knowledge of the informant. It is possible that clues to parentage might be had from the children's names- if they conformed to the naming patterns of the time.
Christine 
Hi Christine,
I've already checked Ann's grave, her husband is not there,
he is not any where else in the Ballarat Cemetery either.
I don't know where Thomas was born.
I checked the shipping records, but their nationality was totally unreadable
Ann was born in Dublin, Ireland.
I have got Ann's death cert, somewhere, I can't put my hand on it at present.
I've already looked up the NSW free online, more than once, but I was hoping someone else could look for another opinion, in case I have over looked it.
Same thing with Victorian deaths, I have searched registers, numerous times, again can't come up with anything, hoping someone else might have ideas what I can do next.
Needless to say after 13 years, I am frustrated and out of ideas.