First, don't know anything about Minix; if it's anything like early x86 Unix/BSD/Linux it will have a Wangtek driver that Just Works (caveat: haven't tried a non-SCSI QIC drive in 20 years...YMMV). Second, there's two parts to this one for DOS:
Driver - you'll need a driver for the card. This will dictate a lot about what runs. Since it's not SCSI, you'...
I don't know where you'd get a copy, and there were multiple non-interoperable backup solutions, but from memory, the TIP (Tape Interchange Program) backup program was one of the most popular for QIC02 tapes.
Common sense says it should have been called TIP-02, but memory insists (possibly fallibly) that it was called TIP-20.