The first published version of the song appeared in Roxburghe Ballads dated 1710; the lyrics were there given the title "The True Lover's Farewell". The song was traditionally sung to a range of different tunes.
In 1907, the composer and folk-song scholar Ralph Vaughan Williams recorded David Penfold, an innkeeper from Rusper, Sussex, singing "Turtle Dove", and the recording is available online via the British Library Sound Archive.
"If I go away I'll come back again..."
Side-note: In recent weeks, when I've started singing this, Yonah has interrupted me with repeated coo'ing. Curious, I tried continuing with it and he continued coo'ing. But when I stopped singing it, he stopped coo'ing. I can only interpret the interruption as him letting me know that he's not fond of this song since he doesn't interrupt any of the others. As with everything, I follow his lead, hints, actions and adjust me, accordingly. I'm not here to dictate or direct, I'm here to support and protect. But since it's part of the original evening repertoire, I keep it included.