If you end up going with a shemagh, as others have suggested, get one from Hirbawi (Amazon Link.) The version they make is very high quality. Also note that their Black+White and Red+White are made from the slightly thicker 220gm/m2 fabric while the less traditional colors/patterns are made from slightly thinner 170gm/m2 fabric.
That said I personally think any physical object, no matter how useful, is a bad idea unless it's been specifically requested. Someone living out of their backpack has likely thought about every single thing in their pack and even the most well-intentioned additional item is unlikely to fit smoothly into that plan. For that reason I'd either ask the recipient precisely what they would want or I'd get cash/gift cards which allow them to purchase something themselves.
Another alternative might be to have her call you after she's been traveling for a while. She'll have a better idea of what's working and what's not and then you might be able to send her a care package with something she knows she forgot or that she now knows she wants.
And if you want to really splurge meeting her somewhere in the middle of her trip might be nice. I know when I've traveled the constant newness of everything can sometimes become fatiguing. Seeing someone from home in the middle of the trip might provide a welcome change.
Shemaugh will do the trick. This one from Amazon is one of the highest quality brands I've found. Very comfortable, they protect from wind, can be wrapped into a ton of different configurations, and work well year round.
When you shop for authentic Palestinian keffiyehs on Amazon, be careful! Be sure to type the name "Hirbawi" in your search.
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I have also purchased Palestinian keffiyehs from Paliroots (Paliroots sells a few Palestinian-themed t-shirts, too)
https://www.paliroots.com/products/classic-hirbawi-keffiyeh
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. . . and from Handmade Palestine
https://handmadepalestine.com/collections/keffiyehs
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. . . and from Shop Palestine, Middle East Children's Alliance (you will find a few Palestine-themed t-shirts on this site, too). Proceeds from sales of all products go to help fund programs for Palestinian children.
https://www.shoppalestine.org/collections/all
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Have fun browsing the beautiful handcrafts made in Palestine!