Just train to carry your pack 6-miles, +3,600' and the rest will take care of itself.
Training for a summer backpacking trip to Mt. Whitney is a lot easier than getting ready for the day hike. The only thing you might want to do it get up to between 12,000' to 14,000' before heading to Whitney Portal, basically to know what to expect.
Head up and over Mono Pass (S) to Pioneer Basin and/or the 4th Recess. With all the snow this past winter this will be a spectacular trip in late July or early August.
