I use inch-thick rubber gym mats, more like puzzle pieces, of the type you link together to form a floor. Over those, I use ordinary mats from Grocery Outlet. The rubber mats don't cover everything. But I got a fair amount of crap on the floor that covers a lot of it.
At any rate, I recently checked again. Last year I had a big mold problem. My dog was a sloppy drinker splashing and dripping water everywhere, and the water bowl was right by the bathroom. The bathroom wallpaper got full of mold. A spot under a window or two out in the main body of my trailer too.
I got a dehumidifier, LOTS of dehumidifying temporary measures(the crystals and all) hung and placed everywhere, and after treatment with spray-on mold-killer, things appear fine again. Dog passed away, no threat of liquid splashing everywhere anymore. No water bowl leaking humidity into the air either. Nor all the dear fellow's constant panting fogging up the place.
Since then, put a fan in the confined little bathroom my small trailer has, plus the dehumidifier and plenty crystal-based stuff. Been going almost two years now. Checked a few times under the inch-thick rubber mats with the carpets on top ... nothing. Mold/fungus gone.
If you are going to lay out carpet and carpet alone, I would suggest using one or two layers of the sort of material that is meant to keep it from skidding. First -- it keeps it from skidding. Hey-oh! But also, it promotes air circulation. Condensation always accumulates, so if you can get some air in there, fantastic. What you want is a system that breathes, from your windows to your bedding to your cabinets to your flooring. Otherwise, every time things cool off, condensate forms and infiltrates everything. It's truly the curse of small-scale, poorly-insulated living. And it's never something you can afford to brush off casually.