I note the IGI has:

QUAYLE, Margaret d/o Willm QUAYLE chr 13 Mar 1778, LONAN, IOM (c.f Maughold)

....So the information below concerning Maughold may not be relevant

Maughold BRs

We can eliminate William QUAYLE, Ballaskeig [1706-1769]
& Wm QUAYLE, B'Allen, bur Oct 25 1736
& probably Wm QUAYLE, Ballellin [1759-1838]

There is a Wm QUAYLE bur Aug 1 1790 (no other detail given) and
Wm QUAYLE bur Feb 8 1804
who would be contenders

I can find no marriage record on the IGI for Wm QUAYLE & Mary KERMODE

Maughold BR has:

Mary KERMOD bur May 16 1818

IGI has:

KERMOD, Mary d/o Wm KERMOD chr 30 Apr 1748, Maughold, IOM