Not sure of the level of backpacking your going to do, flatland or mountain. Or just thumb tripping along the highway, hitting a lot of urban areas. Camping out, hostels (hopefully not like the one in the movie) or whatever.The word backpacking can mean a lot of things. In any event, keep it simple if you do any form of exercise. Can not really plan out a day if your on the move anyway. Focus on bwt exercises. That is, if you have the chance. Hindu push-ups (preformed like divebombers), Hindu squats, dips, chins, one legged squats, step-ups, etc. The usually suspects when it comes to bwt exercises. Might try doing overhead presses, upright rows, straight arm pullovers, curls, etc, etc, etc with that backpack. One or both arms at a time. Can also do short sprints up hills, which affect the legs/calves greatly.
If your doing serious backpackin, like the John Muir Trail, you may or may not want to do any exercises after a full day. If you find the need, than do them early in the morning before the hiking starts. Plan on losing some bwt during the three months. Probably more so when in a higher mountain area. Good Luck.
Side Bar: I've hiked above the Flagstaff, Az area and Yosemite. Nothing like it, great time. Even more fun if you have a female hiking buddy to share your sleeping bag. Good luck.