I had a look at the scan of the 1881 census entry, and there is very little difference between the way the enumerator wrote "J" in Joiner, and "I" in Isle, but on balance I'd guess that Annie was Annie I (with a ditto for Quirk). She was aged 3. So b.1877/78.
There was a slight hook on the J for Joiner, but that might have been because of joining the letter to the following "o" - but Annie I was identical to the I in Isle.
Annie Tate 21 mariner's daughter was written as Yate, as was her son William F aged 4 mo. All born Rushen.
However ANN QUIRK & EDWARD TATE married 21 AUG 1880 Kirk Rushen [IGI extracted record]. I think "Yate" was an enumerator's error.
The 1891 Rushen census has Ann I Quirk servant aged 13 General (Domestic Serv) b.Rushen, in the household of Joseph McCard.
Again it could be J or I, but I think "I".
The IGI has an extracted entry for (her mother?) ANNE QUIRK bapt 1 MAY 1859 Kirk Rushen, Father: JAMES QUIRK, Mother: CATHARINE MADDRELL.
There were these passengers arriving in Victoria (Australia):
Family Name First Name Age Month Year Ship Port Fiche Page
TATE ---- MR 29 MAR 1888 TARAWERA N 222 006
TATE ---- MRS 27 MAR 1888 TARAWERA N 222 006
But where was Edward F? And there were a LOT of Tait/Tate arrivals.