I want to know if a moisture barrier is laid first, can a new wooden floor be placed over an existing wood floor?

I have a peer & beam foundation and am wanting to install new hard wood flooring over the existing flooring, can this be done?

Post and beam? That's the structural timbers. Not that the foundation matters that much, unless you have a lot of moisture from a foundation of stone or block, and a basement floor that is dirt or damp concrete from being poured without a vapor barrier under it. What is your floor made of, and how flat is it? And what kind of hardwood flooring do you want to install, engineered or solid?

If it is engineered hardwood, yes you need a moisture barrier. It is highly recommended for engineered hardwood; it is very susceptible to moisture from under and above.In fact you should never wash engineered hardwood with a wet mop.