This is the 1851 living in Rusholme, Lancashire for the family I suggest is correct:
Thomas Sidebottom 36
Sarah Sidebottom 37
Eliza Sidebottom 14
Mary Ann Sidebottom 12
John Sidebottom 8
Thomas Sidebottom 5
Joseph Sidebottom 3
Thomas is listed as being born in Moston, Lancashire & Sarah, Denbighshire, Wales.
Ancestry UK is suggesting, with numerous hints that only daughter Eliza, possibly son Joseph didn't emigrate to Australia.
I am also seeing suggestions that Thomas's parents were Samuel Sidebottom (Charlesworth, Derbyshire) & Sarah Rowbottom ( Marsden, Yorkshire?), although haven't researched further.