Hi Geoff—I don't know about Patrick, but Hugh McDermott and his wife Mary (née Robinson) baptised a number of their children in Dundalk around that time: Mary Anne (1844), Hugh (1846), Bernard (1851), Teresa (1854), Alice & Bridget (1856), and Jane (1859).
There's a curious gap there 1846–'51, so there's a chance Patrick might've been born in that time and baptised elsewhere (or there could be a gap in the register—I haven't checked for that).