Any plastic or vinyl doll is going to be 1948 and after. I don't know who your Mme Alexander baby is, but she's likely some reproduction or collector doll produced in the late 1960's to 1970's. She could be 80's too, but I'm not entirely sure, but she is made out of a rather rotten line of Alexander plastic that fades terribly and was mostly used mid 1960 and later.
And I've heard other collectors say other things about the 'eye mold,' but that will work to clean it. Doll cleaner and a blow dryer on the eyes will work as well.
In terms of smell, goodluck. Getting scents out of cloth bodies and plastic is difficult at best. Airing them out will do them a world of good, maybe combined with some dryer sheets. The only product I've had good success with in removing plastic odors, including cigarettes, is extremely difficult to track down, and I don't even know if they make it anymore. It was called ZeroOdor and some people have said you can find it at Home Depot or Lowe's, but the stuff was really phenomenal on getting odors out of things that other things wouldn't.