Ditto...........
Great Advice so far..... I've flown from NY (upstate) to out west (CO, NM, AZ, UT, etc.) and never had a problem, so long as I had few days to aclimate. Once got a touch of sickness DRIVING to the top of Pikes Peak (14'200), hiking up that high was much better for some odd reason. Ditto for several other hikes in the 10'500-12'500 range.
If you have the time, take a jog, or brisk walk around Flagstaff (or even better, Sedona) and get a little exercise in the days prior to when you plan to hike and you should be fine. Extra water and listening to your body will help too.
I distinctly remember a few hikes in Bryce NP, Utah (9000') where we were very amused at our high heart rates and breathlessness without any feeling of being tired on a fairly level 7 mile hike/walk.
Have fun, It's a beautiful area.