ON Sale at Mrs. Kearney’s, Fresh Butter at 5s. per lb. where New Milk may be had every Morning at 7 o’clock, at 6d. per quart.
Hobart Town Gazette, 7 November 1818

MRS. KEARNEY informs her Customers and the Inhabitants of Hobart Town, that she has reduced the Price of her Milk to 6d. per Quart; and Butter to 51. per lb.
Hobart Town Gazette, 28 October 1820

MRS. KEARNEY informs her Friends and the Public that on Monday next, she will sell MILK, of the best Quality, at Nine pence Sterling, per Quart.
Colonial Times (Hobart), 14 July 1826

DIED—on Wednesday, at her house in Argyle-street, Mrs. CATHERINE KEARNEY, aged 61, an old and much respected inhabitant of the Colony, having come to it on the evacuation of Norfolk Island.
Colonial Times (Hobart), 9 April 1830

Irene Schaffer has written about her, so I’ll direct you to that.