Per LDS, Ann Quirk christened German 30 December 1838, parents John Quirk and Isabella Kaighen.

1841 census Ballavaish German Ho107/1463/7 folio 9 page 12
John Quirk 65 farmer
Margaret Quirk 65
John Quirk 31
Isabella Quirk 25
Elizabeth Quirk 30
Ann Quirk 20
Eliza Quirk 4
Ann Quirk 2
Eliza Quirk 4 months
John Quine 15 MS
Thomas Quine MS
Esther Gick 6
Note that in 1841, ages of adults were rounded down to a multiple od 5, so John and Margaret could have been 69 in June of 1841.
This gives likely birth years of 1770-1775.
This should narrow down the candidates.

1851 census same address
Isabella Quirk Head Widow 40 Farming 40 acres b Rushen
Ann daur 12 b German
Eliza daur 10 b German
Richard son 8 b German
John son 4 b German
James son 1 b German
David Bright serv 32 unm farm labourer b Ireland
Ann Maddrell serv 19 b Rushen

1841 Corvalla Rushen HO107/1465/11 folio 20 pge 6
Edmond Keggeen 60 Ag L
Jane Keggeen 63
John Collister 35 Ag L
Catherine Collister 35
Wm Keggeen 14 MS
Wm Maddrell 35 Ag L
Ann Maddrell 34
James Maddrell 11
William Madrell Jr 1
Ann Maddrell 9 (see 1851 German above)
Isabella adrell
Jane maddrell
James Cain 3

1851 Corvalley Rushen HO 107 1426 folio 325 page 11
Edmund Keggeen Head M 70 Freeholder Farmer 6 acres b Rushen
Jane wife 71 midwife b Rushen
John Collister son-in-law 44 Mariner b Rushen
Catherine Collister dau 46 b Rushen
James Maddrell grandson 20 fisherman b Rushen

Edmund could be Edmund Keiggeen shristened Rushen on Marc 25 1781 son of William Keiggeen and Isabel Waterson.

On Brian's site check the Kaighen, Quirk and Gawn wills.
Margaret Quirk on film number 0106443 dated 1843, mentions children Eliza. Ann, Margaret, Elizabeth Esther, John and Jane. She names her husband, John, as executor.

There some John Quirk wills, not yet transcribed.