I had a further look for James & Catharine Quirk to see whether anything throws more light on whether they were Annie Isabella's grandparents.
The 1861 Rushen census at Drogedfell? has James Quirk 46 fisherman, wife Cathrine 41, daughters Jane 4, Ann 2, and step son Edward Geale unm 20 fisherman, all b.Rushen.
The 1871 Rushen census has James Quirk 55 Brake? Water Labourer b.Rushen, with wife Cathrine 50, and daughters Jane 14, Ann 12, and Isabella M. 7 - all b.Rushen. There are several Maddrell families nearby.
The IGI has Isabella Margaret QUIRK bapt 18 Jan.1863 Kirk Rushen, daur of James Quirk & Catharine Maddrell. Jane Quirk was bapt 1 March 1857 Kirk Rushen, but her mother is given (in error?) as Margaret Maddrell.
It would be worth looking at this marriage:
James Quirk & Catherine GELL 25 Oct.1856 Kirk Rushen. LDS film no. 0106194, which can be seen through any Family History Centre. These are the Parish register transcripts of Kirk-Christ-Rushen, 1708-1883, and will give you a lot of family information, if we have the right ones.
Edward GELL ("Geale" in the 1861 census) was bapt 14 Feb 1841 Kirk Rushen, son of Henry Gell & Cath Maddrell - so Quirk was her second marriage, and she married as Gell.
Catharine Maddrell & Henry Gell married 29 Feb. 1840 Kirk Rushen.
In the 1841 Rushen census Chathrine Gell 20, Henry Gell 25 Ag L, and Edwd Gell 3 months are living with Jane Madrell 40 Ind., Anne Madrell 15 F S, Harry Madrell 15 Ag S, Elizth Madrell 11, and Margret Madrell 5.
[No relationships are given in 1841, and ages over 15 usually rounded.]
Henry Gell & Catharine Maddrell also had a daughter Catharine bapt 24 Mar.1844 Kirk Rushen. In 1851 at Ballamaddrell, Rushen, Catharine 30 Mar., fisherman's wife, Edward 10 scholar, and Catharine 7, are living with John Gell Wid 85 formerly fisherman. All b.Rushen.
In 1891 Catherine Quirk widow 69 Living on her own means is at Shuan? Pt Erin, with daur Jane S(ingle) 30 Domestic servant, and Jane Hardman grand-daur 4, all b.Rushen.
If this is the same Catharine, I wonder where she was in 1881?