The way I look at it, the minefield usage is that it targets ships physically entering an area. If you QT to inside the range of a minefield, then it would detect you and you'd be subject to the minefields missile attacks. But if your QT traverses a minefield, as long as it continues through and beyond it's range, the minefield would have no effect on you. Keep in mind your QT velocity is somewhere in the vicinity of 20% C or about 60,000,000 m/s so in one second you would be far beyond the range of any missile.
Ideally, to do this what you'd want is to have a quantum interdiction such that an interdiction occurs, and dumps the victim into the minefield. Then they would be vulnerable. Not only vulnerable, but for precious seconds they would not be able to do anything about the situation. That seems to me to be a tall order to set this up, but you theoretically could.