With the QTsi using the Minolta Alpha lens mount, your lenses should work fine with Sony's DSLR and DSLT bodies as they use the same lens mount. Sony's NEX series, however uses a different lens mount so you would need an adapter if you were to go down that route.
DSLRs: Canon EOS 7D Mark II, Canon EOS 70D
CSC: Canon EOS M3
Lenses: Canon EF-S 15-85mm f/3.5-5.6 IS USM, EF 50mm f/1.8 II, EF 100-400mm f/4.5-5.6L IS USM, Canon EF-M 18-55mm f/3.5-5.6 IS STM, Canon EF-M 22mm f/2.0 STM