I would grind out the rust treat it and touch up the bedliner. If you really need carpet then get some on one of the sites. I put some sound heat mat in miy front cab area when I installed the wifes carpet which I have no use for but it is good to go.
To get the rust out use a sander/grinder/wirewheel and take it as best you can to bare metal prime and treat with something there a number of rust products out there. Get some spray can bedliner to cover. It takes some time and patience but needs to be done to at least arrest the rust.
89 2.5 TBI, 4" RC lift, 1" Booms, SYE, Adams Driveshafts front and rear, Ford 8.8 with 4:88s, BFG 33X12.50X15, and a ton of other stuff.
AF Jeep Club Tail Number 184