Egg binding is a possibility and it can actually cause symptoms similar to the ones you are describing, but usually an egg bound quail doesn't live for many days and you should notice it straining, so I don't think she's egg bound. But you can try feeling the area below her vent - if there is something the size and shape of an egg, she might very well be egg bound.
As for how long it'll take for her to start walking after getting her diet corrected - it can be anything from a few days to never. I'd expect to see some kind of change within a few weeks, be it better or worse, but that's as far as I dare guess.