Vinyl planks, plywood, and carpet insulation

Hi everyone, I am new to the site and just started my first home project. I have a 2nd floor 16x12 foot bedroom that had a carpet. I removed the carpet and insulation and currently working on tightning some squeaky areas. I am thinking of installing vinyl planks in this room, but have a concern about noise being transmitted to downstairs, mainly as a result of walking on the new floor. I don't have insulation between the floors, and would like to avoid dealing with that. I thought about keeping the carpet insulation (and perhaps even the carpet as well), and installing thin plywood on top of the carpet, then installing the vinyl planks on top of the plywood. My thinking is that having the carpet insulation layer will reduce the walking noise transferred to downstairs. I would appreciate any advice or thoughts on this. Thanks!