So this morning I set off to find my Thomas Campbell who left the Ballarat goldfields in Victoria for Otago between the end of 1862 and the beginning of 1865, with his wife Elizabeth nee Bratton and his two small sons, born 1861 and August 1862. Thomas and his brother Henry had arrived at the goldfields in 1851 so they had been there for some years.
Thomas and Elizabeth's oldest child, Hannah, born in 1858, died of diphtheria in1861 and together with a greedy local government and a court case they may have felt quite unhappy. Their next child was born in Invercargill in 1865.
Henry stayed on and died childless in Victoria in 1922.
But the family does not miraculously appear on my search. I found that searching year by year returns better results and I do this but did not find them. They could have taken another route, perhaps through Sydney or they may have returned to the UK for a time. I hope you have better luck than I did.