I feel you definitely set an interesting mood and established a solid setting.

My one sole nitpick was "hot breeze caressed." Everything else seemed to evoke a harsh environment so to me the word "caressed" felt too soft for the tone.

I like the tone and the mood of the dryness. You worked it in without beating me up with it.

Dustiest street after trail of dust didn't work for me. Dust is weak. It's usually human skin, and it's something that rests gently on my bookshelf and piano. I realize you're probably looking for adjectives what with the need to use other words like sand and grit and dirt, etc. But I might shift things around in order to reword this.

I visited thesaurus dot com and while I didn't find anything great, there was the word grime, which evoked an image of a kid's face who had been playing in the dirt and with a little liquid mixed in managed to streak his/her face with a finger. Grime is sticky and solid and could work with wiping the sweat to create an image.

"Grime-covered hand" gives you back the word dirt to use elsewhere.

Regarding the wind caressing, I'll take it a step further and have you remove the word "body". A body being caressed implies something you may not be going for at this point. Even if you change caress - for the wind to have any effect on a body it has to touch the actual body.

Lastly, I might remove the bit about contributing from that final sentence. There's a nice hook if you stop at "costing the family too much"

You don't have to hold it long, but save contributing until you're ready to tell us either how she's not contributing, or why. How meaning is she like 11 years old and can't? Or why because she's lazy, or hates working in the mines...

• I would get rid of references to Fremen and Dune.
• I didn't like the flow of the two sentences with the word "mouth" - it's long winded.
• The premise of needing a hat on a desert planet and not having one is too unbelievable.
  

From what was provided, you might start this story as follows:

Nice catch from redux about the "caressed", I agree totally on that. And you could strip away needless information such as: "She felt like the Fremen in the book she was assigned to read last year, Dune. They lived on a desert planet and her zone was desert-like." That first sentence there is awkward, maybe just strip it down to "She felt like a Fremen in 'Dune'." And then you could maybe do away with the second sentence altogether, you've set the scene so well you don't have to resort to this weak telling.

I went back and forth on including the “Dune” reference. I was trying to give a feel for her life and her age without saying, “it’s really hot and dirty and she’s still in school.” I’m not particularly crazy about it, but I haven’t decided if it should stay or go.
I idea of stopping at “costing the family too much” reads much better than the current sentence.

I’m going to see what I can do with these first 13 based on what you’ve said.

The rock skittered along the sidewalk, a trail of dust in its wake. Kell kicked another. Wiping sweat from her brow with a grime-covered hand, she sighed. Canton Street was the longest, dirtiest street in her zone and she walked it every day after school. There were no clouds in the sky, there hadn’t been for months. Her tongue stuck to the roof of her mouth and she closed it, hoping to conserve whatever moisture was left. She felt like the Fremen in the book she was assigned to read last year, Dune.

What she needed, she realized, was a hat. She didn’t dare ask for one though, she was costing the family too much.

She spied another rock, aimed, kicked, and missed; her actions stirring a filmy cloud and coating her already filthy, sandaled feet with yet more of the gritty residue.