Wear a dust mask, close room off to house, open windows and put a fan in if you can. Then cover the rug in heavy dusting of diatomaceous earth, cover that with 6 mil poly, run it at least 12" up all walls, double tape any joints to seal as well as possible. Put down some underlayment to protect the poly, then lay plywood. Vinyl flooring, industrial rubber baseboard, caulk to seal it up to the poly, then trim excess poly if you want. Only thing you'd really have you worry about is trapped moisture, so make sure the grow room floor is well sealed.
Framing a sub floor isn't a bad idea, could incorporate some airflow under it to control moisture. Just lay plywood first or the carpet will get ruined with impressions of the framing, wouldn't have been worth saving at that point.