Pull the carpet up enough to get to the rust, got to tell you 2 ways, amature and professional.

The professional way, cut out the rusted metal and cut a new peice using the rusted peice for a template, hold it in with strong magnets, hard drive magnets would work well, if you have an old hard drive. once the peice is held in, mig weld it in, using only spot welds, but lots of them to keep the heat down, then grind it off and spray a primer then a rust prevenative paint, rustolum would be fine, bottom and top.

Amature fix. Cut a peice of steel, say 18 gauge, make shure it's at least 1" bigger than the rust, arc weld it in.