Shepparton, The Argus, Melbourne, 1 February 1905, p 6, http://nla.gov.au/nla.news-article9884528:

The Rev Dr Skelly, who has been stationed here for four years, has received notice of removal to the Heathcote parish He will be succeeded here by the Rev. Father Delaney of Beechworth.

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Death of the Rev. Edward Delaney, Advocate, Melbourne, 11 February 1905, p 17, http://nla.gov.au/nla.news-article170179377:

We much regret to have to announce the death of the Rev. E. Delaney, lately assistant priest to the Very Rev. Archpriest Kennedy, P.P., Beechworth. The deceased gentleman, who had attained the 35th year of his age, was a cousin of the Coadjutor Bishop of Hobart, Most Rev. Dr. Delaney. The rev. gentleman had been ailing for some months, and it was hoped that a sojourn at the health resort, Queenscliff, would restore him to health. He was for some time in St. Vincent's Hospital, and was, subsequently, removed to a private hospital, East Melbourne, where he received the consolations of religion from the clergy of the Cathedral parish. All that medical skill, combined with careful nursing, could effect was done, but without avail. The patient died on Monday, 6th inst. The deceased gentleman was born in the West of Ireland, and pursued his ecclesiastical studies at Carlow College. He came to the Sandhurst diocese some 12 years ago, and laboured zealously and fruitfully in the parishes of Chiltern and Beechworth, under the Very Rev. Frs. O'Connor and Kennedy respectively. He was to have taken up his sacred duties last Sunday as assistant priest to the Very Rev. Dean Murphy, P.P., Shepparton, in the room of the Rev. Dr. Skelly, who has been transferred to Heathcote. The Rev. J. Gaffy (Myrtleford) and the Rev. J. Ryan (Wodonga) visited their old friend during his illness. Dr. Morsley was unremitting in his attendance. On Tuesday, Archpriest Kennedy came to Melbourne, and had the remains conveyed by the evening express to St. Joseph's Church, Beechworth, where a Solemn Requiem High Mass was celebrated on Wednesday morning for the eternal repose of his soul. The respect in which the deceased priest was held was shown by the large number of priests and people who assisted at the obsequies. The remains were interred in the Beechworth Cemetery. R.I.P.

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Fr T.J. Linane, From Abel to Zundolovich, Vol. 2: Biographies of Priests on the Australian Scene up to 1900, 1980, p 134:

Delany, Edward A., Irish
Popular Student at Propaganda
Many of the old directories spell his name as Delaney. A fair guess would be that he was born in the same county as his famous cousin, Most Rev. Patrick Delany of Hobart — next to figure in these pages — viz., Galway. He studied at St. Patrick's, Carlow, and at Propaganda College in Rome. Volunteering for service in Sandhurst he arrived on the 'Austral' in October 1894. Placement for the first few years is not recorded, but probably he was kept under the episcopal wing in Bendigo itself. From '96 to '98 he was assistant at Myrtleford and from '98 to '01 served at Rutherglen. Then came a transfer to Beechworth. Illness dogged his steps for many months and so he was confined to St. Vincent's Hospital in Melbourne. On his sick-bed he received notice of appointment to Shepparton, but death came his way before the changeover on 6 February 1905. Burial took place in Beechworth. And if more information is required the one to convey it would be Miss Grace Maguire of Myrtleford.
(Footprints, Vol. 3, No. 7)