I have found records of John Palmer LEEDER senior and Blanche Case coming to Australia on the 'James Gibb' in 1849, however John Palmer junior is not listed as a passenger in the online records, but his death certificate indicates that he came to NSW at roughly the same time as his parents.

NSW BDM Death Registration Number 1891/013695

Date and place of death: December 31st 1890 at 34 Carabella Street, Borough of North Sydney
Name and occupation: John Palmer Leeder, Custom House Officer
Sex and Age: Male, 59 years and 11 months
Cause of Death: a) Epithelioma of Leg and Femoral Glands b)Asthenia
Duration of last illness: 2 years
Medical Attendant: C.L. Clark S.R.C.P M.R.C.S etc.
When he last saw deceased: December 23rd 1890
Name and Occupation of father: John Palmer Leeder, Gentleman
Name and maiden surname of mother: Blanche Case
Informant: TH Leeder, Son of Deceased and occupant of house in which dceased died. Carabella Street, Borough of North Sydney
Particulars of registration: 1) Jas E. Webber 2) January 2nd 1891 3) Arthur Street, Borough of North Sydney

When and where buried: January 2nd 1891 St. Thomas' Church of England Cemetery, North Sydney
Undertaker: Wood and Company Undertakers
Name and religion of Minister: S. H. Childe, Church of England Minister
Witnesses of burial: T. H. Leeder, W. F. Leeder
Where born and how long in the Australasian Colonies or States: Norfolk, Enland, 40 Years in New South Wales
Place of marriage, age and to whom: Sydney N.S.Wales, 22 Years, Annie Shillington
Children of marriage: William Frederic - 36 years, Thomas Henry 34 Years, John Shillington 31 Years, Charles Edward - 25 Years, Arthur Ernest - 19 Years, Willie Alfred - 17 Years, 3 males dead.