Yes, Oates is mistranscribed as Gates. The IGI birth record indicates September 1843, and baptism October 1843 (St Georges). The birth record was obtained some time ago and I am unable to locate this same record in the present familysearch.org IGI index, and I am also concerned with the inclusion of St George in this same birth record. Does this not imply a christening record? A note - Frederick's second christian name is recorded as both Walton and/or Walter.

Frederick Walton Wilson
Birth: 04 Sep 1843 St George Douglas, Isle of Man
Father: Robt. Wilson
Mother: Elizabeth Oates

name: Frederic Walter Wilson Gates
event: Christening
event date: 04 Oct 1843
event place: Douglas (St George's), Isle of Man
gender: Male
father: Robert Wilson
mother: Elizabeth Gates