If it's really fired ceramic, then it will be too hard to machine on your setup. But you could easily machine a slab of unfired ceramic and then fire it. This works best when the clay's at the "leather-hard" stage, about a day after you roll it out. But this isn't a quick process; firing takes more than a day, and you need to let the clay dry thoroughly before doing it, which takes about a week.
Have you tried machining plaster of Paris? You can cast it any shape you want, and it machines pretty easily. It's not expensive (a 50 lb sack costs about $20) and it's fairly resistant to heat. There was a formulation of gypsum plaster that was meant for carving; it's discontinued now, but all it was was plaster and some PVA glue, which held it together somewhat so it made chips rather than dust. That stuff made a mess when carved before it dried, since it stuck to everything, but regular plaster can be carved 24 hours after casting with no ill effects.