No problem buying 1mm end-mills if you want to have a go but they're easily broken.
Tricky to use because home machines are rarely fast enough : a 1mm end-mill should be run at 10,000 rpm or faster. 50000rpm would be good!
When feed rate exceeds cutting speed, the work snaps the cutter. And it's difficult to keep the feed-rate low enough to suit a 1mm end-mill spinning at only 3000 rpm. Low rpm on small cutters and drills make them sensitive to any hint of operator clumsiness.
At 10000+ rpm, the end-mill cuts fast enough for the feed-rate to become manageable, otherwise develop a delicate touch! Worth looking at the spindle motors used for engraving machines and CNC if a lot of small diameter work is planned 12000rpm seems typical, faster the better.
I'd make the occasional tool described it by drilling a 1mm hole and grinding off as the other posts say.
When the cutter is made, note that it too will work best at high rpm. If finish is poor, try speeding up and/or reducing feed-rate.
Don't have much experience of delicate cutting work like this. Much breaking, bending and poor finish when I try. More practice might fix my problems. Can you report back how your experiment works out? I might learn summat!
Dave