A 3yr gap between birth and baptism would be extremely unusual at that period - the old Roman catholic tradition would still hold in that the vicar would baptise privately (ie at home) the sickly child - there might then be a gap before reception into the congregation but both acts should be noted in the register (this sometimes accounts for double entries in the IGI though most vicars/parish clerks actually noted the reception with a side note as to an earlier private baptism) - in earlier Bishop's visitations a question would be asked as to whether the vicar did attend to this private baptism and how many times a year.