According to his death Certificate, Edward was born around 1843 in Lisheenfroor. HIs parents were Thomas Quealy and Bridget Haugh. 

Edward Quealy married Margaret O'Neal/O'Neil in New Zealand in 1881. 

His wife's obituary contains some helpful biographical information for Edward:

Obituary - MRS. MARGARET QUAILEY.

Mrs. Margaret Quailey, for many years a well-known and highly-respected resident of Woollahra, died on Tuesday, 6th inst., at the residence of her daughter, Mrs. Robert Curtin, Duxford-street, Paddington, with whom she had been living for the past few years. The late Mrs. Quailey was born in County Limerick, Ireland, 66 years ago. In early womanhood she sailed for New Zealand where she married Mr. Edward Quailey. For a time the young couple were engaged in agricultural pursuits in New Zealand, but eventually came to this State about 44 years ago, when Mr. Quailey entered the employ of the Woollahra Municipal Council. During her long residence in Woollahra Mrs. Quailey was noted for her active participation in every movement for the cause of religion and charity, and her kind and gentle nature drew to her a host of friends. Though Mrs. Quailey had been ailing, for some years it was not until within the last month that serious symptoms manifested themselves.. The immediate, cause of death was pneumonia, which supervened an attack of influenza. Her passing was peaceful and happy, for she had all the consolations of her holy faith, ad ministered by the Rev. Father P. B. Lawler, O.F.M. She was also - visited during her illness by the Sisters of Charity, from Paddington and Woollahra. The late Mrs. Quailey, whose husband predeceased her in 1917, has left a grown-up family of four sons and four daughters to mourn their loss. They are Messrs. Thomas Quailey (Lidcombe), .Jack Quailey (Kensington), Edward Quailey and Frank Quailey (Paddington), Mesdames Robert Curtin (Paddington), Harold Elliot (Kensington), Jack Curtin and George Taylor (Paddington). The funeral, which left St. Francis' Church, Paddington, on the Wednesday morning, was large and representative. Among the mourners was Mrs. Maguire, of Lidcombe, a life-long friend of the deceased. Rev. Father M. -P. Kelly, O.F.M., officiated at the grave 

Edward Quealey died December 18th, 1917.

Funeral Notice:

QUAILEY - The friends of Mrs. MARGARET QUAILEY, also EDWARD and FRANCIS QUAILEY are kindly invited to attend the Funeral of her beloved HUSBAND and their dear FATHER Edward to leave his late residence 20 Holdsworth street, Woollahra THIS THURSDAY, at 2.30 for Catholic Cemetery Waverley Sydney Morning Herald (NSW : 1842 - 1954), Thursday 20 December 1917, page 5

(The AHC Guild[1] announced) The death is announced of Bro. Edward Quealey a very old and highly respected member of Woollahra branch, at the age of 74 years. His remains were interred in Waverley Cemetery, Rev. Father P. B. Lawlor officiating at the grave. A widow and a grown-up family are left, to whom the sympathy of a wide circle of friends is extended.— R.I.P.

 

[1] The Australian Holy Catholic Guild was a society of Catholic laity established to promote Catholic interests and solidarity across the colony. The society was founded in 1845 by John Bede Polding, first Roman Catholic bishop and Archbishop of Sydney.

Additional Information
Date of Birth 1st Jan 1843 (circa)
Date of Death 18th Dec 1917
Father (First Name/s and Surname) Thomas Quealy
Mother (First Name/s and Maiden) Bridget Haugh
Spouse (First Name/s and Maiden/Surname) Margaret O'Neal/O'Neil
Place & Date of Marriage in New Zealand in 1881
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