How is your bird?
Do you feel an egg in there too - or is it just tissue (prolapse)?
I don't know anything about quail, but took a quick peak at the quail forums...it looks like you can treat her like you would a chicken.
Soaking in epsom salts is good. Apply a little hemorrhoid cream to help reduce swelling. Offer her some calcium and vitamins.
If she has an egg stuck as well, you can try applying a bit of ky jelly or something similar to see if that helps lubricate.
Having what looks like 2vents, I fear the intestines are prolapsing as well, unfortunately if the intestines are coming out too, you may not be able to save her.
Keep us posted.