Our speaker of "Barbie Doll" sounds like she's straight out of a modern fairytale and on a mission to turn the whole damsel-in-distress motif on its head. The girlchild is a kind of Sleeping Beauty, only a prince isn't coming to wake her up from some awful nightmare. (Bummer.) Instead, in a rather macabre but modern way, the speaker makes the girlchild look like a victim of the world around her without any practical way of defeating the wicked witch or undoing the evil spell. And Prince Charming is certainly nowhere to be found.
So the speaker tells the girl's story in the same sort of way we might hear Sleeping Beauty's story, only her "happy ending" involves a casket, a putty nose, and a creepy nightie. We hear the girlchild's story through the speaker's third-person omniscient point of view, again similar to the kind of voice you'd hear in a fairytale. The really macabre portions of the poem involving the girl's mutilated body also sound a bit like a tale out of Grimm's Fairy Tales, but we notice that the speaker has a larger message in mind regarding societal pressures and the absurd adult world. So Piercy's poem isn't just about freaking us out with witches that eat kids and such.
Essentially, the speaker sounds like a cross between the speaker of a classic fairytale and a speaker of some sort of feminist treatise. It's a weird mix, but it works in this poem. We hear the poem's classical elements balanced with a more modern perspective. She also has a kind of dark humor that's impossible to ignore when reading lines about "pee-pee dolls" and "wee lipsticks" followed by the "magic of puberty." The humor comes to us through the speaker's sarcastic tone that captures the absurdity of the adult world in which the girlchild finds herself. The very last line in particular ("To every woman a happy ending") demonstrates the speaker's sarcastic point of view perfectly, since we know there's nothing "happy" about a young mutilated girl in a casket.