Welcome to the forum, Greg, and congratulations on your new trailer!
Replacing the carpet is a huge job, and will keep the trailer out of commission for a good while during prime season. Have you thought about just steam cleaning it, multiple times if necessary, and camping in it this year? For one thing, you'll find out if this is really your perfect trailer before you invest substantial time and money in a major rehab project.
If you do eventually replace it, one option is what Scamp
uses: a layer (or two) of foil-bubble insulation ( e.g., Reflectix) covered with marine hull liner (a thin mildew and stain resistant carpet-like material). You pretty much have to gut the inside and remove windows
to do a neat job of it; that's what makes it such a major project.
Best wishes with whatever you decide!