The father in this [1871] census looks like John James son of James Quine & Cath Corlett bapt Maughold 6 Jan 1841.

Problem is that son James appears in the 1881 census with the family as John J., so couldn't be James Edward the apprentice baker aged 18 at 7 Albert St Douglas.

John James QUINE Head M Male 41 Maughold, Isle of Man, England Miner At Lead Mns
Margrett QUINE Wife M Female 50 Lonan, Isle of Man, England Wife
John J. QUINE Son U Male 16 Lonan, Isle of Man, England Miner At Lead Mns Son
Thomas QUINE Son Male 14 Lonan, Isle of Man, England Scholar
Edward FARAGHER Border U Male 25 Lonan, Isle of Man, England Lead Miner
Source Information:
Dwelling Glen Rd 81
Census Place Lonan, Isle of Man, Isle of Man
Family History Library Film 1342346
Public Records Office Reference RG11
Piece / Folio 5601 / 70
Page Number 25

Any other James or Edward Quines in the 1871 census b.c.1863 in Laxey/Lonan?

Sue