Anna, there's not an obvious connection though it would seem likely the Kirkups of Stannington and the Kirkups of Rothbury would be related.
My ancestor, Robert Kirkup, was a farmer from Rothbury. He is believed to married a member of Clan Douglas (or at least the English side of the Clan) in about 1750. As far as I know, they had three daughters and no sons. It was my Browning ancestors that migrated to Australia.