I believe the 1802 date hearkens back to "The Frolicksome Irishman," which seems to be the precursor of the other ballads. The earliest copies are dated roughly as 1802-1819, probably closer to the latter.
It was sometimes printed on the same ballad sheet as the "Kerry Recruit," but with words about Balaklava and the Crimean War of the 1850s.
The "Frolicksome Irishman" starts out with similar verses to some versions of the songs printed later:

About nine months ago I was digging the land,
With my clogs on my feet and my spade in my hand,
Thought I to myself it's a pity to see
Such a genius as I digging land by the way.
(nonsense refrain)
I pull'd off my clogs, shook hands with my spade,
And away to the fair like a roving young blade
I met with a sergeant, he asked me to list,
With my great gramachree give me your fist,

He'd give me two guineas...etc.
(He gets into battle, but succeeds in getting back to Ireland to dig murphys again).
Firth c14(116), and others, printed in London, Bodleian Collection.