Belts would be fine, but you have to have them far thicker than you would have thought... that then eats into the cost saving. For the price of some c7 rolled screws from china these days I don't really see why you'd use belts. It's not like your axis is too long for screws.

Dremels are also a pretty bad choice in almost every regard, not least that when cutting carbon fibre they will blow the dust around even more than it already will be, and CF dust is nasty stuff for humans and machinery. My first machine had a proxxon router which is similar to a dremel but with better bearings, still blew through two of them in fairly short order once I asked it to start machining FR4/G10 and CF.

If Carbon fibre is on the menu, you really need to think about dust management which really ultimately ends up with cutting underwater. For that, a spindle that doesn't blow air everywhere (ie a water-cooled spindle) is really ideal... bonus is that they are also far more quiet. Even HEPA filters on Vacs can't guarantee you'll trap all those pesky CF fibres. A company I did some work with had no end of problems with their prototype electronics for months, eventually traced it back to them having a new CNC machine that they had been using to prototype CF frames for drones - despite the vac shoe and hepa filter on the shop vac, enough still escaped to settle on their PCBs and components to cause serious misbehaviour. They switched to cutting underwater and had a top to bottom clean of the lab, no problems since.