I was mistaken "kittled" means "have a litter of Kittens" in Scottish... at least at Burns time.

The song seems to have been popular.   Here are a few recorded references:

CAT THAT KITTLED IN JAMIE'S WIG, THE. AKA and see "Miss Lyall." Irish, Highland. Ireland, County Donegal. A Dorian. Standard. AA'B. A popular highland in County Donegal, recorded by fiddler John Doherty. In Scotland the tune is known as a strathspey called "Miss Lyall." Source for notated version: John Doherty (1895-1970, County Donegal) [Feldman & O'Doherty]. Feldman & O'Doherty (The Northern Fiddler), 1979; pg. 80. Green Linnet SIF 3077, John Doherty - "Bundle and Go" (originally recorded for Topic Records). Green Linnet SIF 188, Patrick Street - "No. 2 Patrick Street" (appears under the eroneous title "Hard by Seifin").

Is Australian & Irish/Scottish tunes the same?