It appears simply as "New Song, No. 38" in Timothy Connor's song book, written while in prison during the American war For independence (George G. Carey, ed. A Sailor's Songbag: An American Rebel in an English Prison (Amherst: University of Massachussetts Press, 1976), p. 107-108.

The date given for Connor's entry is September 4th, 1778. In his notes, Carey cites Bell's contention that "the song may have spun off an actual event that happened during the reign of Elizabeth," but he offers no other information on this point and wrote that Connor's song "was clearly taken down from a broadside slip." (P. 109)


Here are a few North American variants, the first from Pennsylvania by way of Kansas . . . .


THE DOG AND THE GUN

The was a young squire from yarmouth was here
He courted a noblemans daughter most dear
And for to get marryed it was there intent
All friends and relations they gave there consent

The time being appointed all for the wedding day
A young farmer was chosen there waiter to bee
As soon as this lady the farmer she spied
It inflamed her heart o my heart this lady cryed

She turned away from him but nothing she said
And instead of getting marryed she went to her bed
The thoughts ove the farmer still run through her mind
And away for to get him away she did find

Coat vesket and small clothes this lady put on
And a hunting she went with her dog and her gun
Oftimes did she fire but nothing did she kill
Till at length the jolly farmer came whistling in the field

Ohe I thought you would have bin to wedding she cried
To wait one the young squire and to bring him his bride
Oh no replied the farmer the truth to you I will tell
I wont give her away for I love her to well

This lady being pleased for to see hime so bold
She gave hime her glove it was all flowered with gold
She told him she found it as she came along
As she was a hunting with her dog and her gun

This lady went home with her heart full of love
And she gave out the speach that she had lost her glove
And he who will find it and bring it to mee
I will adoar him forever his bride I will bee

As soon as this farmer the news he came to here
Strait away unto this lady in haste did appear
Saying here honered lady I have found your glove
And will you be so kind as to grant me your love

Tis already granted this lady replied
I love the sweet breath of the farmer she cried
I will be mistress of my dry apailing of my cow
While my jolly brisk young farmer goes a whistling to his plow

The day of the wedding she told of the fun
How she hunted the farmer with her dog and gun
But now I have got him so fast in my snare
I will adore him forever I vow and declare

Written   William A. Larkins / May the 18th A.D. 1866

Source:
Ruth Ann Musick, "The Old Album of William A. Larkin," The Journal of American Folklore, Vol. 60, No. 237, (July-Sep., 1947), p. 228-229.

Notes:
"When William A. Larkins started his 'book of all songs' in April, 1866, he may not have realized that he was making a valuable contribution to folklore. Like Chaucer's young squire, he was twenty years of age at the time, and did considerable singing 'when called upon by his friends.' Evidently he wrote these old album songs down to sing at such times." (p. 201)

Musick notes that Larkin's family was originally English, settled in Pennsyvania and moved West, first to Ohio and then Illinois. It was in Pekin, Illinois "that he recorded his book of songs." Larkin often performed at Grange play parties, and "was well known and in great demand."



Here's a fragment from Kentuckians who settled in Wisconsin . . . .

THE LADY WENT HOME WITH HER HEART FULL OF LOVE

The lady went home with her full of love
And sent out the news that she had lost her glove
Saying, 'Who will return my glove to me,
I vow and I declare their bride I will be."

Now they are married she tells of the fun
How she hunted up her farmer with her dog and gun
She picks up a her basket, goes milking of her cow
While her brisk young farmer goes whistling at his plow.

(with tune)

Source:
Asher Treat, "Kentucky Folksong in Northern Wisconsin," The Journal of American Folklore, Vol. 52, No. 203 (Jan.-March, 1939), p.36

Notes:
"Sung by Pearl Jacobs Borusky, July 13, 1938. Cf. Sharp, The Golden Glove."

The author goes into some depth regarding emigrant "Kentucks" who, along with Polish and Bohemian immigrants settled in northern Wisconsin and scratched out a living

"Perhaps their tenacity to their southern way of living contributed to the cultural isolation of these people. They had known backwoods life before. They knew how to hunt, fish, cut timber, and scratch the cheap land enough to raise a little corn, a few hills of beans, and maybe some potatoes. But a certain uneasiness and distrust toward them was often manifested by their northern neighbors. Their names, their speech, their manners, their cookery- many things made them seem different from the others; and even now, when many are of the second or third generation of the Wisconsin born, some of those differences persist." (p. 2)


Albert Tolman also printed a text in JAF, vol 29, no 112 (April-June, 1916). I'll track that one down tomorrow if I get the chance.

Pauline Greenhill included it in a discussion of Newfoundland cross-dressing ballads ("'Neither a Man nor a Maid,": Sexualities and Gendered Meanings in Cross-Dressing Ballads," The Journal fo American Folklore, Vol. 108, No. 428 (Spring 1995), 156-177).

Nothing I've seen indicates any magical subtext or origin earlier than the second half of the eighteenth century.