I've climbed Cirque Peak twice the last 4 years, however, for me, I tackled the peak from New Army Pass. From the pass just followed the flat ridge all the way around. It is easily a nine hour hike, or 15 miles.
Keep in mind, that on the decent, the PCT is just below. So head down, somewhat southeast and you pick up the trail.
Since you leave your car at Cottonwood Lakes trailhead (head over New Army Pass)and you return via Cottonwood Pass trailhead, take the equestrian trail which junctions at Trail Pass cutoff. Once at the pack station (about a 1/4 mile), just stay to the left and at the end of the horse turnouts head toward the equestrian campsites and viola, you are back where you started.
Last year when I climbed Cirque, I left at 7am, (took the South Fork shortcut), was on top of New Army at 10:30. I was on Cirque (after stopping to watch a herd of bighorn sheep sidle by), at 12:15.
I was back at the car by 4:45pm