Dust, Musk, and Moth wings.

[dukealien]

The carpet is made of green vines and Persian silk, soft as a baby's cheek, a butterfly's whisper, the touch of a feather that sends ripples along a puddle, on and on until it makes the paper boat rock violently back and forth, makes the paper bleed grey and crumple slowly, slowly inwards with the help of an invisible giant's fist until it is nothing more than a floating body, a sodden island for ants and minnows. 

First paragraph, an extended simile.  I'm unconvinced by paper bleeding gray unless it was originally white - which is unstated.  First image of leaking gray, probably oily but nonetheless without oil-rainbows, is not supported... but there it is.  Say white paper, or say otherwise.

The carpet store smells of musk, perfume and dust, a moth flutters its damp wings along the dim walls of the basement, a few weak lights casting long dark shadows along the walls, flipping both hands on top of each other, it's easy to project a a turtle on the wall, or a wolf, or a butterfly, as bartering floats by, the words dressed in euphemisms, our carpets are the best in the world, and suddenly you can picture Aladdin himself riding on the deep blue rugs, his handsome knees leaving half moon crescents embedded in the pattern of the fabric, but Jasmine doesn't appear because the store keeper is yelling to get down from the stack of carpets, not to touch them with dirty shoes, his nose wrinkled at her black runners with pink bottoms and velcro straps, and she shrinks into the walls smelling of petrichor, watches her parents examine the carpets as a third person narrator.

"Bartering floats by" is arresting:  excellent.  Introduces a new element... which is not pursued when Aladdin intrudes and runs the table.  Commercial aspect returns briefly with the store-keeper's brush-off.  (Lost me at "petrichor" but I looked it up - sounds a bit more chemical than its definition, but does sound.)

Her mind won't be quiet, exotic birds freeze mid chirp with their beaks agape and she traces their wings with her fingers, leaving deep grooves that she know will make the store keeper angry, but maybe if she traces hard enough, the birds will break free and fly like paper angels falling through their cookie cutter cuts. She hides behind a mountain of circular carpets, spots the dead carcass of a spider hanging from its web in the corner, she crouches by it and blows gently, then runs away when its hollow body shudders ominously on the web, but does not move. A baby wails from its stroller and she peeks behind the carpets, pulls her tongue out and make faces, and the baby stops crying abruptly, watching her with serene, reproachful eyes. 

"[R]eproachful" is the surprise here, wonderfully irrelevant but perfectly visible.  The rest is joyfully trying to bring life from inanimate (even presumably corpse) matter.  More could be done with the spider (cast-off exoskeleton, its next life still being lived nearby, web as its hard-spun rug).  But the length of the passage is already ample.

But alas they settle for the itchy green carpet with coarse hair and her mother will spend several hours a week washing it and vacuuming it, but the fabric will still pinch and poke like hideous little thorns when they all sit down with their linen pyjamas, and the buttery flowers, although stiff, feel nice against her finger, as she digs her index in the centre until her mother snaps at her to stop. The carpet has a life of its own, and the leaves seem to grow a few inches everyday, although nobody believes her, but there will come a day when the paper boat sets sail once again and the fabric will lose its edge and become dulled once more, soft and docile as hay.

Again, a fine finish ("docile as hay") which could refer to coming docility of the followed character, combed every day (like the rug, like the girl-child's hair) by her mother.  Because that's what mothers do.  "[F]abric" for a rug is somewhat technical but also subsumes all made things into rug and child.

This is wonderful in a very slightly stereotyped way.  New rug, young girl; bartering - and too soon the matchmaker, the dowry, the bleeding paper boat.  In intensive critique, I have little to add and - more to the point - little that needs cut.  It is, of course, a short story or vignette rather than a poem as we would usually picture - but it is certainly a prose poem with much fine embroidery.

Can the parents be more fully described, the shop-keeper more threatening, the bartering more combative?  Maybe.  But would the viewpoint character notice those things?  Less than the spider's abandoned tapestry.  Maybe that's the way to go:  even longer musing on the butterfly and the web.

So, perhaps, not much help on improvements.  But it was a delightful, even exhausting, short ride.

P.S. Just caught on about the reproachful child.  What the viewpoint character hides beneath it all?  Subtle.