which Irish uprising ? - 1698 or 1798 ? - after that (and you quote 1823 birth in Cork) there was the potato famine 1843 onwards - the next uprising was the 1916 followed by the Irish civil war in 1922/3

There was transporation to Penal colonies in Tasmania and NSW (australia) late 18th thro to c.1840 (some a little later) but they generally had to have done something however small to justify it; and court records will exist though the Irish Civil war saw many destroyed as the 4-courts record office was used a bomb factory (I have an excellent article describing this for those interested)

Shortage of Time and genealogy are very poor bedfellows !