How do you let your baby "air out" or go diaperless?

Over the summer if my baby got a diaper rash we would let her just lay out in the shade in the backyard with no diaper on. Letting her air out like that would always heal the rash. For about 24 hours now though she has had a pretty bad rash, I've tried Desitin which usually works for her but it hasn't gotten better as fast as her rashes normally do. It is too cold outside to let her be in the yard, so I'm thinking I'll just let her crawl around our house without a diaper for an hour. I'm just a little hesitant because our house has brand new carpet and hardwood and I will be a little sad if she pees or poops on it 😅 is there anyone who lets there baby go diaperless who has a solution for this?

Btw I am not worried about yeast infection or anything, she just has a rash because we tried a new brand of wipe that she had a reaction to. Obviously not using the wipe anymore.