The parish of Bride was sparsely populated in those times, the only John Crowe was ch 1805 and Ann Callow ch 1803 but no sign of marriage or ch. of Elizabeth. In 1833 Mary Anne Crowe was registerred to them and in 1856 Elizabeth Anne Crowe was christened to Elizabeth Crowe (no father mentioned). By 1881 Elizabeth Anne Craine was living with her grandfather John Crowe still in Bride- the name presumably that of her father-, but no sign of the others.
So by deduction Elizabeth existed but you need the help of others with census around 1851-61.