Elizabeth you seem to be short on answers so i'll comment on the later years of your message.
By 1851 there were no Qualtroughs remaining in Lezayre most of this group had moved to Andreas. Jane Dougherty wife of Daniel was running a lodging house in Larivane -seaside of the village-with her daughter Catherine and another son called Robert Sayle, Blacksmith age 21.Living with them were grandsons Harry Gilbater 12 and Thomas Gilbater 8.
Jane's son John (1817) married Emma Freeman Thompson and had a number of children listed on IGI. He became chaplain of St. Judes in Andreas.
Jane died 1861 and Catherine took over the lodging house. By 1881 she was living with her son James Dugdale - the right age for James Alexander. My guess is that each of the children took the surname of the father hence the disappearance of the name.
Between the mother and daughter you have collected a variety of names to work on, especially Gilbater.