This strikes me as a surrealist poem. The following definition, although overly simple and reductionist, can be of some help here:
Surrealist work: a work of art, all the elements of which are
recognisable as representative of real-world phenomena, but where there
is something impossible about how those elements relate to each other.
In accordance with this, we recognise every element in the poem as being something real: the shiny feathers, the act of making something, the bird, its roundness, the cage, the big airplane, etc. However, when it comes to putting these things together, the realism evaporates: Starting with only feathers, we are asked to create a huge, round bird — an airplane, in fact — in which we can travel with our loved ones, over the hills and far away, while singing its praises.
If this resembles a dream, it’s because it probably is. Surrealist art is often seen as a reflection or interpretation of dreams, and of the subconscious generally. That also means that surrealism does not seek to convey a specific meaning: we are free to read into it whatever resonates with us. A reading of the poem as the depiction of a place of happiness for a family or a group of people who love each other absolutely makes sense, but basically any other interpretation is possible.
