How is your quail chick doing?
If you have a few pictures of her leg, that would be quite helpful. Or a video of her trying to walk. In case you're unfamiliar with how to post a video, you'll need to upload it to a video platform like Youtube or Vimeo, and copy/paste the link here,
https://www.backyardchickens.com/threads/how-to-attach-images-under-construction.1399465/
Poultry can suffer from several leg problems, including slipped tendons, varus-vagus deformities, riboflavin deficiencies, incubation malpositions, and genetic abnormalities. regardless of the problem, it's generally recommended the bird be put on vitamins, specifically riboflavin (B12) to address if it is indeed a nutritional problem and to support overall healthy leg growth and function. That would ultimately be my first suggestion, then, doing a quick overview of what you're keeping her in. Slippery bedding such as hardwood flooring, newspaper, slick wood, metal can caused their legs to slip outwards also known as "splayed legs".
It could also be some sort of genetic abnormality, or possibly a malposition while she was in the egg that caused greater muscle pull to one side of her legs than the other. Or something such as slipped tendon which can be caused by a wide variety of things ranging from nutritional problems to trauma, or malposition. These problems tend to be harder to treat than the earlier ones mentioned above, and often require a trip to the vet for surgery if the hock joint is swelled, or unable to bend properly. The surgery will likely be costly and may or may not work. It often consists of an incision done on the hock joint, where sutures are put in to fuse the periosteum to the trochlear ridge.
If caught early, sometimes the legs can be manipulated back to place, where a hobble or external coaptation device can be implemented to correct the deformity. This would best be performed by a vet, as if the leg is manipulated too much the leg can lose blood flow, or swell considerably.
https://www.merckvetmanual.com/en-c...ctious-skeletal-disorders-in-poultry-broilers