Sounds like a great hiking trip! In terms of preparation, the best thing you can do is increase the size and strength of your aerobic engine. Developing a stronger aerobic engine means you can maintain your normal pace at a lower heart rate, delivering oxygen to your muscles with less effort.
While hiking with a pack is an essential part of preparing for a hiking trip, youre going to want to spend some time working out at a higher intensity level. You could do this via running or speed-hiking, but the key is to get out of your comfort zone and push the pace to the highest intensity you can maintain for 10-20 minutes at a time. After 10-20 minutes of running or speed-hiking, switch to a gentle jog or walk for eight minutes before going back to a faster pace.
The goal is to gradually increase the total amount of time you can spend at your maximum sustainable intensity. This will increase the efficiency with which your aerobic system can deliver more oxygen to working muscles. Increasing the efficiency of your aerobic system at low elevation will give you increased ability to meet the demands of low oxygen at high elevation.