And a bit further c1800. From ECCO (Eighteenth Century Collections Online). From the BL but I don't have the reference.
Cupid's Magazine being a Choice Collection of New Songs Sung at Vauxhall, Ranelagh, the Theatres and all Places of Public Amusement.
24 songs of which this is the 3rd.

Molly's Lamentation

Farewel, farewel my Polly dear,
Ten thousand times adieu
for I must cross the raging seas,
Savages to subdue.
Come change your ring my dearest,
Come change your ring with me,
To be a token of my love,
When I am on the sea.
And when I am gone, dear love,
And know not where thou art,
A letter unto thee I'll send,
With secrets of my heart
All secrets of my heart, dear love,
And best of my good will,
For let my body be where 'twill,
My heart is with you still.
Altho' from England I must go,
All into foreign parts,
If e'er we meet the savages,
We will shoot them thro' their hearts,
The crow that flies so black, so black,
Shall change her colour white,
If ever I prove false to thee,
Bright day shall turn to night,
Bright day shall turn to night, dear love,
The rocks melt by the sun;
If ever I prove false to thee,
The sea and land be one.
Now farewell my dearest dear,
I can no longer stay,
For seven years, alas! I'm bound
To sail to Bot'ny Bay.

The 'If ever I prove false' stanza is a commonplace dating back at least to the 17th century. Some very un-PC language in this version. No wonder it was dropped for later versions.

So like many others it probably started out as a theatre piece or at the pleasure gardens.