This poem is a lyric poem, except, of course, that it is not one person telling us about themselves but a group that speaks using the first person plural, "We." When we think about the form of poetry, a narrative is a story told normally by some form of omniscient narrator, a sonnet is a fourteen line poem with a strict rhyme scheme and structure and a monologue poem is a poem that is a long story told by one person.
A lyrical poem is a poem that is normally short and brief, and a poem that is of a song-like quality. The alliteration and the rhyme serve to make this poem definitely song-like in its presentation. Just read it out to hear the song-like cadence of the rhythm.