She is telling you she doesnt want to toilet outside and would prefer to do it inside - so it has to be a litter tray I'm afraid. Its always a good idea to keep a tray indoors anyway, even for cats that normaly toilet outside. You can get non dusty litters now, the wood pellet ones like Lady Rogue mentioned, not sure how the silica ones would be for someone with asthma, but they are not dusty.