Since we're dealing with Barbie and miniature GE stoves, it's safe to assume that we're in North America somewhere, although we don't get any specifics. Of course Barbie exists in other places too, but considering how normalized "pee-pee dolls" and the like are in this poem, we get the feeling we're definitely in the good ol' U.S. of A.
But we notice that we're also in a child's version of America since we feel and hear the girlchild's point of view. We get to experience the joys of puberty all over again along with the added bonus of being teased by classmates. We also see just how absurd and out of touch the adult world really is for the girlchild, which makes her side of the story so much more real to us.
Of course the fairytale vibe of "Barbie Doll" provides an extra-creepy twist when imagining the poor girl dead and mutilated in her casket. So we have a kind of dark fairytale version of America that takes place in an already confusing childhood world. And yet it all comes together rather nicely (though gruesomely) by the end in a way that sums up the absurd expectations for all women, young and old, in America.