...but the salesman might have said that he would pay the VED as part of the deal....so he would be doing the "taxing" for you. Hadn't you better ask him?
If they're going to do it for you they would have had to ask you for your insurance certificate, so it looks like it's down to you but still worth checking.
As above, plus you can't tax it until it's insured anyway. (When you tax it online the system automatically checks the motor insurance database to ensure that a valid policy exists for it):
https://www.gov.uk/vehicle-tax