A Prayer-Calendar of Deceased Priests & Deacons in Australia 1788-2009, compiled by W.T. Southerwood, Sixth Edition, 2009, p 89: Hartley, Bathurst, etc, NSW; Ballarat, Vic. Listed as "P. James Dunphy, died 15 July 1845".

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The Ordination, Australasian Chronicle, Sydney, 23 August 1843, p 2, http://nla.gov.au/nla.news-article31740880:

On last Sunday the sacred rites and ceremonies prescribed in the "Pontifical" for the ordination of Priests were impressively performed in St. Mary's Cathedral, when the following deacons--John Grant, James Dunphy, Patrick Maginnis, John Kenny, and Patrick Hallanan--were duly invested with the holy and indelible "character" of the Christian Priesthood. The Archbishop used for the first time in his Metropolitan Church the PALLIUM; this is the especial mark of affection and confidence conferred by the Chief Christian Bishop on earth on other Prelates, who hold the most responsible position in the Church next to the Sovereign Pontiff himself. The "PALLIUM" is only worn in conferring Holy Orders, and on a few solemn Festivals of Religion. The Vestments or Robes used by Bishops and Archbishops when officiating in "Pontificals," include the respective vestures of the several orders from "Acolyte to Priest," together with those belonging to the "Episcopal" order, to represent that the Prelate possesses the plenitude of each of these orders, with the "Power" to confer them. To a superficial observer this multiplicity of vestments worn at one time would appear quite superfluous, and savouring of worldly pomp; but there is nothing--not the slightest ceremony in Religion, without its moral or mystical meaning; these are the silent and impressive symbols that speak to the eye and to the mind, and not unfrequently convey more lasting impressions to the soul than the most fervid eloquence.

The Vicar General preached a very instructive Sermon, pointing out the solemn ceremonies instituted by the Almighty of old for the consecration of Aaron and the Levitical Priesthood, which was only a shadow and a figure of the higher and more holy "Priesthood" of the New Law, and showing the propriety and consistency of using sacred rites and ceremonies in the ordination of the Priests, who are to serve under the Perfect Covenant of Grace. He gave a graphic description of the duties and responsibility of a Christian Priest; of his voluntary separation from the spirit of the world; of his tearing asunder all the ties of flesh and blood, that he may devote himself entirely to the dispensation of the "Mysteries of Christ," and to the sanctification of his own soul and of those committed to his care. He then pourtrayed the duties of the flock towards its pastor, in hearing his voice and following his instructions, and that they should look rather to his sacred character than endeavour to decry those minor faults which are inseparable from man in "this vale of tears;" and concluded by a moving appeal to the five deacons who were then going to undertake a spiritual burden to be dreaded even by Angels. This is a mere outline of the discourse. We have heard several express a wish to see the whole in print, though the Preacher himself appears quite averse to the proposal. The Church was crowded by an attentive audience during the whole service, which lasted more than three hours.

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Death of the Rev Mr Dunphy, Morning Chronicle, Sydney, 26 July 1845, p 2, http://nla.gov.au/nla.news-article31745985:

It is with feelings of extreme regret that we have to announce the premature and awfully sudden death by drowning, of the Rev. James Dunphy, which melancholy event occurred on Friday, the 11th inst.

The reverend gentleman had been out in the discharge of his pastoral duties, and was returning to Bathurst; but in endeavouring to cross the Mudgee River, by some means unknown, he appears to have fallen from his horse, and was lost. He was seen to go into the river by a shepherd who was at a short distance fron the place and soon after disappeared and was seen no more. The body of the unfortunate gentleman was not recovered until the following Monday.

Mr. Dunphy was a native of Kilkenny, in the diocese of Ossory, Ireland, and arrived in this Colony with the Very Rev. Dr. Ullathorne, in January, 1839. He went through his ecclesiastical studies in St. Mary's Seminary, Sydney, and was ordained to the priesthood about two years ago. His mild and unassuming manners, his gentlemanly deportment, and urbanity of disposition endeared the reverend gentleman to all who knew him, and his death will be a source of great affliction to his numerous friends and beloved flock.

On Tuesday next, a solemn mass for the dead will be said in St. Mary's Cathedral for the Rev. Mr Dunphy; and also for the repose of the soul of the Rev. Mr. Macarthy, whose anniversary it is on that day.

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Patrick Francis Cardinal Moran, History of the Catholic Church in Australasia, 1895, pp 119:

Among the papers of Father Therry, there is a letter of young William Dalley, from Sydney, dated the 30th of July, 1845, which, whilst written in schoolboy style, gives a few interesting particulars:-
"I am very sorry to state that the Rev. Mr. Dunphy was drowned in the Mudgee River. He was compelled by duty to cross the river on horseback, it being in a flooded state. When about half way across the river, the under current threw the horse down, and, as the reverend gentleman could not disengage himself, he was drowned. A shepherd on the opposite bank saw the whole of the fatal accident, but could not render the least assistance. High Mass was offered up in St. Mary's Church for him on Tuesday, the 29th instant, by His Grace the Archbishop, assisted by the Right Rev. Dr. Epaille [Epalle], Vicar-Apostolic of Western Oceanica."
(p 205) The 31st of December, 1838, witnessed the arrival in Sydney of the Vicar-General, Dr. Ullathorne, accompanied by three priests--Rev. P.B. Geoghegan, O.S.B., (subsequently Bishop of Adelaide), Rev. Richard Marum, and Rev. Thomas Butler, and three ecclesiastical students, MM. Dunphy, Magennis, and Grant. With him also came a community of the Irish Sisters of Charity, the first nuns that devoted their lives to the work of religion in Australia. Never perhaps had such an eager and joyous congregation assembled in St. Mary's as that which filled the sacred edifice and all its approaches on New Year's Day, 1839. The friends of Dr. Ullathorne rejoiced at his return to the colony after an absence of two years and a half. The well-wishers to religion welcomed the accession of three zealous priests to the ranks of the clergy. But, above all this, the whole body of the clergy and faithful, in unison with their chief pastor, exulted in the arrival of the devoted Sisters of Charity, to whose advent the Bishop had so long looked forward as his main hope for the reformation of a considerable number of the convict class. Pontifical High Mass was celebrated at St. Mary's, the newly arrived priests and nuns were grouped around the altar, and many were the fervent prayers offered in thanksgiving to heaven for the most opportune spiritual aid thus brought to the Australian Church.