The vet did that???
You NEVER cut the quick no matter how long the nails are. If the nails are overgrown you have to start trimming a little at a time until the quick is back up where it is supposed to be. If it had only been a month since his nails were last clipped they should not have been that bad.
I'm sorry but I would not let that vet within a mile of any of my pets. Are you using a stypic pen on the poor little doll's nails? I cannot imagine a vet, of all people, doing such a cruel thing to a dog!
Most dogs that have had the quick cut, even accidentally, never forget that experience and are terrified of having their nails cut afterward. My condolences to you and your little doll.