You know I always was told a cat bite or scratch for a bird was lethal even by a vet, who treated a Quaker parrot of mine many years ago and the parrot died.
So 2 years ago one of my cats who is mostly feral outside got a baby cardinal out of a nest and ran off with it, it was a bit chaotic and I ran after the cat who I then told to drop the baby and he did, in front of a neighbors door.
I grabbed the baby, and I took it inside, and I cleaned it’s wound on the wing with water and antibacterial cleanser like I would my own skin. It was a small bite mark but the wing was injured, there wasn’t a lot of blood. I crushed one of my left over antibiotics after researching what would be used if brought to a vet, I don’t have an avian vet I am my own avian vet, and the vet I do use - uses google.
So I think what’s the point of me trying to dish out all this money to treat a bird at a normal vet who uses google and knows less than I do, I crush the pill up into dust, I mix it with wet cat food, I do this for a week, and in between that I also hand fed it wet cat food every few hours like I would feed a baby parrot bird formula with a syringe to fill its crop. Only I used wet cat food instead as I read it’s better for wild birds.
I’m not telling you to follow my advice or feed it this, what I’m saying is how I personally saved the bird after the cat got it. It’s still alive 2 years later in fact he’s in the kitchen. He has a special diet, and he’s on 3 different vitamins. I’m trying to get his color to come out and his feathers to properly grow out. So I keep trying different things.
My point is they say a cat is fatal but it isn’t always fatal, as I’ve proved in saving this baby cardinal who was only 10-12 days old.
My advice is to treat it as you would any wound, and keep in mind that since it was a cat it probably does have a better chance to become fatal. If you have some kind of bird antibiotic maybe you can use that or google what a vet would use which is what I did and I’m not going to say here what that was as I am not a vet, nor do I remember what it was I used. It did however work. At least in this case.
I can’t promise it will work for anyone else.
Just do your best. That’s all we can do after all

I hope your quail makes it ok!!