For a supposed song, this poem is distinctly un-song-like – unless, of course, it's a song by Bob Dylan, who doesn't care so much about rhyming or rhythm or any of the other formal regularities that make it easy to sing along to that snappy tune on the radio.
Sure, the poem is divided into six three-line stanzas, but the stanzas don't have any rhyme scheme or distinct metrical pattern. Even the line breaks seem to follow regular patterns of speech more than then correspond to a Master Plan. Perhaps that's a way for Plath to assert how utterly new and strange this "song" is – and we're betting that, in fact, the lack of form might be a way to indicate that new experiences (like, say, birth and motherhood) require new forms.
Plath is experimenting with poetry as confession – an incredibly intimate, soul-revealing, emotion-baring sort of confession. After all, she's telling her child that, well, she doesn't necessarily feel all those warm fuzzy feelings that mothers are "supposed" to have. It might just be that trying to superimpose a fixed poetic meter on top of words that are supposed to come from the heart would dilute some of the poem's immediacy. As it is, we feel like she's shedding all sorts of conventions in order to express what she really feels – and things like meter and rhyme happen to be among those conventions.