Opened 1837. Apparently extended 1859. (Addition of tower/entrance?).
Sign in front of the tree says:

St John The Evangelist
Catholic Church
1836
Australia’s Oldest Existing Catholic Church
MASS TIMES
1st & 3rd Sunday of the month 8.30am
2nd, 4th & 5th Sunday of the month 11am

On Sunday last divine service was celebrated by the Right Reverend Dr. Polding, Catholic Bishop of these colonies, in the house of Mr. Cassidy, at Richmond. After an eloquent and fervent exhortation from his Lordship, the congregation entered into a subscription for the erection of a Catholic Church in that township, when the very handsome sum of 535l. was immediately obtained. This, it is expected, will be very considerably augmented by the donations of several gentlemen, of other sects, but friends to religion and morality indeed, by all who are desirous to see the rising generation of colonists educated in their duty to God and their fellow men. A most eligible site has been pitched upon near the bridge, for the erection of the sacred edifice, and for the forming of a burying ground; about four acres of land having been liberally presented for these purposes by Mr. Cassidy, in addition to his munificent donation of 200l.
Hobart Town Courier, 28 August 1835

CATHOLIC MEETING AT RICHMOND,
AT a public meeting of the Members of the Catholic community of Richmond and its environs, held on Monday the 21st inst. at the Lennox Arms Inn, for the purpose of adopting measures for the erection of a Catholic church in that town, the Rev. J. A. Cotham in the chair, the following resolutions were agreed to.
Resolved,
I. That a committee be formed of five members, and that the said committee consist of Messrs. J. Cassidy, R. Troy, R. Gavin, S.M’Cullock, and Andrew Counsell.
[continued]
Hobart Town Courier, 2 October 1835

Hobart Town Courier, 1 January 1836

Colonial Times, 2 January 1838 (I take that to mean the opening dates as the 31st December 1837.)

CATHOLIC CHURCH, RICHMOND.
We have been requested by several subscribers, members of the Catholic faith, to publish the following which appeared in a morning contemporary yesterday :

This Church, which has been considerably enlarged and decorated, was re-opened this morning. High Mass was performed at 11 o’clock. Present the Bishop, and the Revs. Dunne, Hagon, Keohan, Marum, Bond, Fitzgerald, Ryan, Murphy, Woods, and Hunter. Mr. Hogan sang High Mass, assisted by Mr. Bond and Mr. Fitzgerald. Mr. Del Sarte presided at the Choir, assisted by Messrs. Hunter and others. The Church was densely crowded in every part, and members of every denomination testified their affection and respect for the Catholic Pastor of Richmond by assisting at this interesting ceremony. The appearance of the Church and altar was beautiful in the extreme. After the Gospel, a most edifying and instructive Sermon was preached by the Bishop.
…
The Rev. Mr. Dunne then spoke as follows :-He knew no words which would be sufficient to express his thanks for the cordial manner in which they responded to the proposal of his health. When the heart was full it was difficult to find words to give due expression to its feelings and sentiments. That he felt proud on that day, that he rejoiced exceedingly it would be utter affectation to conceal. He regarded that day as one of the proudest of is life, when a work to which he had devoted many an anxious thought, and many a toilsome hour, had received the solemn benediction of the Church, and when he saw himself surrounded by so many dear, liberal, and generous friends who approved, by their presence, the good work that was done, and gave encouragement to all who had taken part in its accomplishment. To himself, he believed, a measure of praise had been extended in relation to that work entirely out of pro portion to his merits. It was true he desired that a church in which he had ministered so long and so unworthily a Church which was first erected by the Catholics of this colony, should be not only so enlarged as to accommodate his congregation, but should as well, exteriorly as interiorly, exhibit some ecclesiastical style and architectural beauty. To compensate for his own deficiencies, he de sired that some work which would be permanently useful to his people should be executed. Moreover, he thought the house in which the Almighty was worshipped should be the grandest and most beautiful of all houses, and believed the beauty of the house of God had a powerful influence in nourishing the piety and refining the minds of those who prayed and worshipped therein. He therefore desired much that such a work should be done, and seeing its necessity, determined with God’s help to accomplish it. … He protested it was not he who made these improvements. The design was furnished by Mr. Frederick Thomas, and subscriptions for the whole work were contributed by persons of all religious denominations as well as by the members of his own flock. He was glad, however, for the sake of the Richmond district, of which he was now if not an old, certainly a middle aged resident that such a building has been erected. Richmond, in his, opinion, equalled if not exceeded any other district in the colony in the mildness and salubrity of its climate, as well as in the romantic beauty and picturesqueness of its scenery, and he was very glad that St. John’s Church, as it now stands, proved that the people of Richmond were as liberal and generous as the scenery amidst which they resided was naturally beautiful and romantic.
Hobart Town Daily Mercury, 15 February 1859

TASMANIAN CHURCHES
St. John’s, Richmond
Oldest Catholic Church in Australia
(By W. J. Rowlands.)
St. John’s Roman Catholic Church, Richmond, the site for which was given by the Cassidy family, is the oldest existing Catholic Church in Australia.

As will be seen by the illustration, the building is a substantial stone structure, of beautiful design, and good workmanship, that has stood the test of time remarkably well, considering that nearly a century has elapsed since it was erected. In 1835 the foundation stone was laid by Dr. Polding, and Father Cotham placed in charge. Governor Arthur allotted £500 towards the cost of construction.

“The old church,” writes a former resident of Richmond, “with its stained glass window of exquisite colouring, takes rank with the best country churches in Tasmania, and brings back to me vivid memories of my childhood. The district, with its sunny, open spaces, and the glory of its sunrises and sunsets among the hills, which, to east and west, bound this fine expanse of agricultural land, has a peculiar charm, and close beside the little old-world town is the substantial bridge.”

Inside the church there is a painting of the “Adoration of the Magi,” purchased in England by Father Therry for £200.
The Mercury, 27 January 1930

View from church.

The cemetery is behind the church.