I-140 processing time primarily depends on 2 factors:
1. Category file under (EB1/ EB2/ EB3/ or something else)
2. Service Center filed with (Calif/ Texas/ Nebraska/ Vermont)
Points 1 and 2 above will determine the approx time to get I-140 approval. It can be anywhere from 2 months (EB2 for Calif) to 11 months (EB3 Vermont). But I totally agree with Rajeev that it is atleast averaging 6 months.
If you can answer 1 and 2 then it will be easier to determine how much time it would take for your I-140 approval assuming there is no RFE. Let us know 1 and 2 for you.
As far as immunization records, most of us do not have them. Like your case, my wife and I have had chicken pox when we were small but have no record of it. I will tell the doctor when i go for the immigration medical checkup and do as the doctor says, which may mean taking an additional shot, which is fine.
Disclaimer: I am not a lawyer. My replies are based on knowledge gained on immigration sites & my studies on US immigration. It is always good to consult an immigration attorney such as Rajiv Khanna. If you have specific questions for me, please PM me.