Hello

[Kitwn]

Nathan,
Welcome to the forum. I also make clocks but with wooden wheels rather than brass and probably a bit larger than yours. You'll find all the help you need for building a suitable machine available here.
For designing clocks and producing the code needed to drive the CNC router I can strongly recommend the 'gearotic' software by Art Fennerty available from the link below.
The main difficulty you will have with using a CNC router for cutting clock wheels is the very small diameter of tool you will need for small teeth. Sub millimetre cutters are available but you will need to build a very rigid machine with low backlash and runout to keep from breaking them within seconds. A cheap OTS machine may not be good enough. The gearotic software tells you the maximum diameter of tool you can use for a given design. If you download the trial version you can see if your intended sizes are practical for cutting in this way.

https://www.gear2motion.com/

Kit