I think that the iconic reference to Barbie is quite evident in Piercy's poem.  The construction of the Barbie Doll by Mattel is used to reference how women's identities are constructed by a patriarchal society.  In this light, the presence of Barbie as an icon is something that has been absorbed by women and the social order that relegates them to the status of the doll.  Piercy makes this present in the opening lines of the poem.  While we don't see the Barbie doll, it is present in the first 2 lines that girls "are presented with dolls that did pee- pee."  In this seemingly harmless act, Piercy is bringing out the idea that women's vision of self are constructed from the earliest of ages. The presence of "lipsticks the color of cherry candy" enhances this feel, as well. Women learn early on what society believes they are and this message is reinforced throughout their lives.  Just like the Barbie doll who is constructed for particular aims and to represent a particular state of being, women's identities are constructed in much the same manner.