Last time I was in Moab in October it was hot (mid 80's) in the desert sun, and the nights were gloriously cool. You cannot beat zero humidity and 40's to 50's at night with the rock slowly cooling underneath you at night.
Since you are in Flagstaff, think about conditions more like Sedona or even a bit lower elevation than that. Moab is around 2,500 ft on the canyon floor, the canyon rims are a couple thousand feet above that. I wouldn't worry about getting cold. I'm in Colorado Springs, and at about 7,000 ft. our climate is fairly identical to Flagstaff (you guys don't get quite as warm, but average lows are identical). Think early Fall and add 10 degrees and you'll have typical conditions, i.e., this is the perfect time of year for Moab. What you probably love about September in Flagstaff is what you'll love about Moab in October.
Nay