I have an Office Professional Plus 2016 account on my PC. Can I now install Office on my laptop with the same account?
You do not have an Office Professional Plus 2016 account… There's no such thing. You have registered at most one Office Professional Plus 2016 license on your Microsoft account with your name, so that will not work. As a rule, your license can only be used and activated on a PC, as long as you are not a company and have a volume license.
This transfer and use of licenses across multiple PCs is only possible with an Office 365 subscription.