1mm is relatively large for such a small drill.
You could try drilling a 1mm hole in 2 or more steps.
When drilling a large hole in steel you usually centerpunch, center drill, drill the hole in several steps.
This is due to drill geometry:
The web of the drill doesn't actually cut material all that much. So when you start a hole the web causes the drill to wander about.
Often you can drill a small hole (larger than the web size of the large drill) first, because a small drill has a small web, which means you can sometimes get away with not drilling a centerhole first.
After this the web on the larger drill will not "cut" any material. (it will rotate in the small hole)