From the Madden Collection of broadsides (via Steve Roud), apparently about 1820:

                                DOODLE DOO


        As I was a going along London streets,
        A handsome frigate I chance’d to meet,
        She was well rigg’d and fit for sea,
        And all she wanted was my money.
                                Lal de fal la, &c.

        She took me to a little house,
        The door and window as snug as a mouse
        She gave me kisses by one and two,
        And ask’d me to play with her doodle doo.

        I am a barber by my trade,
        And many a wig in my time I’ve made,
        The first I made it was a scoff,
        The tail I burnt and the wig flew off.

        She went unto her father’s hall,
        Down on her bended knees did fall,
        Pardon daddy and mammy too,
        For I’ve been playing with my doodle doo.

        Your doodle doo, pray what is that,
        It’s rough and hairy like a cat,
        It’s rough and hairy and split in two,
        That’s what I call my doodle doo.

        Her mammy said, what do you mean,
        You saucy, brazen, impudent quean;
        I certainly will make you rue,
        For playing with your doodle doo.

        O mother do not be in a rage,
        Before you was fifteen years of age,
        You left your father and mother too,
        And follow’d my dad for his doodle doo.

quean = whore

scoff = "an object of scorn, mockery, or derision" (Merriam-Webster).

"Frigate" suggests a song sung by or intended for sailors.

The speaker of stz. 2 is not clear.

The song concludes in the manner of "The Long Pegging Awl."