That's probably a sign of illness or severe infection. Isolate her from any other birds, keep her warm, and try putting some apple cider vinegar in her water. Hopefully someone who's seen this behavior before in their own quail can weigh in with more specific help.
Mareks disease can cause "drunkeness" in poultry, a contagious viral infection. Botulism from bad feed can also cause stumbling, paralysis, etc...although death comes quicker with botulism than with Mareks. Poisonous plants, or even antifreeze can cause this symptom. Neurological issues from birth or even encephalitis's like West Nile, WEE or EEE can cause drunkeness.
My king quail hen had this. She fell over and walked like she was drunk, turns out she was laying a shell-less egg. She even fainted... Unfortunately there are no avian veterinarians in my area, so it is fully my responsibility to take care of them best I can.
So I increased the magnesium and calcium intake, I put her in a warm and dark spot. Everything was fine within 1-5 hours.