Well it sure looks authentic from the photos.
The movement and case numbers which I believe do match up, indicate 1960-65 vintage.
I believe that's when the 1071 and 1072 (with date function) started to be used.
The other marks indicate swiss made (I belive that's a key on the right) and the profile of a woman's head indicating made in Canton of Geneva.
The writing underneath Vacheron and Constatin is a bit cryptic to me. I think it says "SW" +some numbers but I dont know the significance of it.
The dial may also have had the word "Automatic" printed on it.
There is one model: Reference 6727 which has the identical case, crown, and a similar dial but with a date window at 3 o'clock and used the 1072 movement. It was built in 1963 and sold in 1965. It also had a Geneva seal. I'm willing to bet, looking at the movement that yours has one too, but its likely hidden. So its clearly from that era.
But unfortunately, it does need a bit of restoration work. There must be some master watchmakers in Israel who can restore it. But if not, you can send it back to Geneva, to the Boutique and they will transfer it to their restoration department at their factory.
It will take a few months to get a quote and the time period to restore it depends on the amount of work required. It can take quite a while!
PS: If you do want to send it back to VC, Alex or I or many other people here would be happy to provide you with the required info.