Transformer fuse for primary coil. 240V with 16VA
Does that mean I need to get a 100mA fuse?

Yes, a 100 mA fuse should do the job.

There are fast (F) and slow (T) fuses, I would start with a fast fuse and see how that works out. If the fuse would sometimes blow when the transformer is connected to AC mains then try again with a slow fuse.