So lethal vapors destroys any creature that comes into play. Considering the fact that stuffy doll is indestructible lethal vapors shouldn't destroy it if I cast it after lethal vapors is in play right?

Stuffy doll cannot be destroyed. Lethal vapors destroys creatures. Logic dictates that stuffy doll does not get destroyed.

The destroy effect from Lethal Vapors will still target Stuffy Doll, but the destroy effect won't actually do anything.