I'm unsure - probably the Willian who was a teacher was probably William Davis who married Sarah Mayers and emigrated to NSW to teach. The minister of the parish (Warrenpoint and Clonallan) who baptised the Davis children was himself the Rev'd John Davis. Was he a cousin? Brother? He was not much older I think than our William Davis the emigrant.
Was the baker a relative? Hard to say in either case as it's not an uncommon name.