Hi anonymous,
9437/1976 NICHOLLS JOSEPH ERNEST DIED LIVERPOOL 084
His birth appears to be in the NSW BMD too...
19092/1891 NICHOLLS JOSEPH E JOSEPH BESSIE LEICHHARDT
As is his parent's marriage...
2289/1884 NICHOLLS JOSEPH LOGAN BEESIE CANTERBURY
He appears to have a number of siblings, including Roy, recorded too...
5924/1885 NICHOLLS JOHN JOSEPH BESSIE ASHFIELD
4926/1887 NICHOLLS ARCHIBALD E JOSEPH BESSIE LEICHHARDT
6878/1889 NICHOLLS CONSTANCE E JOSEPH BESSIE ST PETERS
19092/1891 NICHOLLS JOSEPH E JOSEPH BESSIE LEICHHARDT
5962/1894 NICHOLLS ROY E JOSEPH BESSIE BATHURST
10928/1896 NICHOLLS THALMA G B JOSEPH BESSIE BATHURST
5581/1898 NICHOLLS ALBERT R B JOSEPH BESSIE NEWTOWN
Based on some Google search results that I haven't had time to follow thro on it appears that Bessie and the Logan family arrived in Australia on the vessel "Boyton" in May 1877.
Unfortunately, coincidentally there was a Joseph Nicholls who perished on the Titanic and search results are hard to filter as a result.
Good Luck.