A treadmill set to a 10% to 15% incline is great for getting your legs and heart trained for long stretches of climbing. However it doesn't do a complete job.
First, it's a lot different going uphill on a flat surface at a constant incline and pace than it is on a trail that's anything but flat and even.
Second, while this may exercise the muscles you need to go uphill, it does nothing for the different muscles you use on the way down.
To deal with all of these issues, see if you can find a hill in your area. It doesn't have to be high because you want to go up and down several times a session. For added exercise carry a backpack full of weight, e.g. sand bags or gallon jugs of water, etc.
And as others have already said, you need to be acclimated to the altitude, especially at 10,000' and up (although that varies by individual.) For that all I can suggest is arrive a few days early then go on daily hikes of increasing length, ascent/descent, etc. If you've trained well at home you'll get acclimatized that much faster.
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