There were several possible candidates for the Thomas Quirk who married Ann Elliott Bennett in 1792. Do you know the names of their children and birth years ? The only one which comes up in a casual IGI search is Elizabeth Hooper Quirk b 1795. If she was the eldest daughter, then Thomas Quirk's mother may have been called Elizabeth.

Here are a few records I've copied for you:
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marriage copied from IGI:

Name: Thomas Quirk
Spouse's Name: Ann Elliott Bennett
Event Date: 1792
Event Place: Wyke Regis, Dorset, England

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Baptism:

Name: Anna Elliott Bennett
Gender: Female
Christening Date: Dec 1772
Christening Place: Moreton, Dorset, England
Father's Name: Joseph Bennett
Mother's Name: Mary

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Baptism of one of their children:

Name: Elizabeth Hooper Quirk
Gender: Female
Christening Date: 25 Jun 1795
Christening Place: SAINT NICHOLAS STREET-INDEPENDENT,WEYMOUTH,DORSET,ENGLAND
Birth Date: 10 Apr 1795
Father's Name: Thomas Quirk
Mother's Name: Ann

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A possible marriage of Ann Elliott Bennett’s parents perhaps ?
Name: Joseph Bennett
Event Type: Marriage
Event Date: 02 May 1771
Event Place: Piddletown, Piddletown, Dorset, England
Spouse's Name: Mary Hooper

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The only IGI baptism I can find for a Manx-born Thos Quirk with a mother named Elizabeth:
Name: Thomas Quirk
Event Type: Baptism
Event Date: 13 Jul 1750
Event Place: St Matheus Chapel, Braddan, Isle of Man
Gender: Male
Father's Name: Jno Quirk
Mother's Name: Elizth Moore

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Could this “will” summary be relevant ?

Braddan: 1778-2 E d QUIRK Thomas departed isle 13yrs ago + not heard of;bach;fa john

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And this ?

1761-2 E d QUIRK Elizabeth MOORE d 23 dec 1760;ch thos,ann,john,cath + robt - all ua uncles john + thos moore + thos corlet with cath sayle als moore supvs;husb alive

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I'm just throwing out possibilities here----nothing concrete.

Jean C