This is most intriguing - the plot thickens!! There's a Stephen Rynhart married 1839 to a Mary Miller and who lived at Listerlin, near Inistioge. In same year a Mary Anne Rynhart married a William Miller.
I had at first thought the Millers came from the New Ross/ Inistioge area but then shifted moer to thinking they came from near Enniscorthy as that's where Henry & Eliza Miller are recorded in 1842 - there are also Millers on Abel Ram estate near Gorey in 1813 and 1836.
But it seems from your info, that this Jacob Miller was born Inistioge area and that his parents then must have subsequently moved up to Enniscorthy - a good distance in those days. I wonder could Mary Miller above and possibly William be related to Henry & Elizabeth or to your Matthew Miller?? If she was, it would help explain why Stephen Rynhart moved down (as I think) to that area to live. As an aside, there's also an Eliza Leach or Leech, father Matthew Leach, I think from Killeen near Inistioge who marries a John Rinehart same period, lived at Listerlin and emigrated also to Aus in 1854 - definitely the place to go at the time!!
I've also been in touch with another Miller in Australia, who is descended from a Joseph Miller born 1789 in Wexford who left for England and whose son, Jabez Miller emigrated to Australia. This Joseph would be contemporaneous with Henry Miller and Matthew Miller, I think?
Any insights appreciated - with a bit of collective effort, we might yet unravel!
Barry D