Whirk? Also try Whirt, Quirk or Whirter (or saying it in Scottish and Irish accents to get the phoentic spellings).Lots came from Isle of Man and jumped back and forth, not so far away from Wigtown area.Check www.familysearch.org for following:
Daughters of John Whirk: Isabella, b 1785, Inch Margaret, b 1783, Inch Agnes (yours?) b 1791, Inch Elizabeth, b 1793, Inch.
Also try www.scotlandspeople.gov.uk to search OPRs for births and marriages.Suggest do search on All OPR records first - to see how little there are!Will need to register plus costs but reasonable.
Have in our tree a Susan Whirk who married James Gibson on 15 june 1811, Stoneykirk (near Inch).Her parents were John Whirk (but not birth cert for Susan exists in Scotland), and Grace.Parents names taken from Susan's death cert but maiden name of mother missing.James Gibson is son fo William Gibson and Elizabeth Rodie married c 1774, Stoneykirk.
There is probably a connection somewhere (the Gibsons were also jumping back and forth from Isle of Man), but my Susan Whirk is not in my direct line so have not spent time on her.