Don't they all?
All my cats do or have done so. Barf. Wretch. Hurl. Toss. Heave. Chuck. Upchuck. Download. Vomit. Spew. Blow chunks. Toss cookies. Unswallow. Spray-paint the carpet. Yawn in technicolour. Drop a gastro grenade...pick your term. It's part of what they do. Not my favourite part, but I don't think this pet supply store has the answer, either. Our cats barf when they eat grass. Sometimes to chuck a hairball but that's rare.
No! Not on the carpet! On the hardwood! Aw, &*#^!!!
More synonyms for puking.