, congratulations on your purchase and welcome to the Forums!
I have a 1963
Overlander which has many similarities with yours, and I've just begun a frame-up restoration of the back half of my trailer. These trailers tended to leak a lot through the back window and around the rear bath, so I suspect you'll need to replace at least the back sheet of subfloor, or you can alternatively think of that as the rear 4'. I'm going to go ahead and replace the rear 8' (two sheets), because I'm adding a gray tank as well (Airstream did not include gray tanks before around 1974 I believe).
To determine where you have floor rot, open every cupboard you can, and take an ice pick or an awl and push it into the floor. Anywhere it penetrates, the wood is rotten. Try to get as far our toward the outer shell as you can, because that's usually where the most damage is from leaks. If they are only very small areas of rotten wood (a few inches across), then you might be able to get away with patching it using a product like Rot Doctor. If they are as big as a foot, sometimes people are able to cut out the bad sections and scab in new plywood. But if your rot issue is several feet, then you're going to need to replace entire panels of subflooring.
You should also try to remove carefully the bellypan in the rear area, and inspect the frame. Chances are you'll have some frame rot (heavy rust that eats through the metal, rather than only superficial rust). If you do have frame rot, then you should cut out the old rusted steel frame pieces and replace with new material. If you don't have access to welding equipment, you'll need to take it to a shop. After you address the frame issues, then you can put in a new subfloor and replace the bellypan.
I'm not trying to scare you, but these old trailers tend to have these problems, especially at the rear end. Much better safe than sorry.
I think the absolute best place to start, for anyone who is about to do a major renovation job, is with the major renovation threads. I've linked them below, and some of them are lengthy, but read as much as you can and most of your questions will be answered.