I would try to check the original of the birth certificate.

There is no male Quayle, occupation draper, in the 1901 census.
If there were I would expect him to be resident in Ramsey not Ballaugh.

I think you'll find that the family you want is that of Robert Quayle & Ann Isabella Craine who married 19 Apr 1859 at Ballaugh.

Plug the names into the IGI search at www.familysearch.org and you'll come up with at least 4 children.

The family are in the 1861 census at Ballaugh when Ann Crain is listed as mother in law, aged 65.

The family are not in the 1871 census - ?off the island.