I don't know that there is one that everyone would agree on.
https://coturnixbreeders.com/standard-of-perfection
These folks claim to have a working draft, but I'm not sure how much weight their organization carries. I also don't think they'll show you their draft without becoming a member, which seems a little unusual to me, but I already confessed to not showing, so maybe I'm just not familiar with modern practices.
I also don't know if they require a few for membership, nor how that works.
Why did you want a standard of perfection, if I may ask? If it is for a show, I'd ask who ever is promoting the show what standard they intend to use.
If it is for developing your own breeding program, I think most quail breeders either go for weight, or for egg production, or for whatever feather traits they like. All white, dark, red, feather sexable, etc etc. In other words there's probably a reason why there isn't already a well known SOP.
Best wishes!