You would NEVER want to use 1/1600 sec in a low light situation, because it's too fast a shutter speed and ALL of your images would be a blurred mess.
The SD880 IS is a point & shoot (fully automatic) camera, so you cannot set your preferred shutter speed other than a long shutter/exposure of between 1 and 15 seconds (1"-15"). And for that, you would need to mount your camera on a tripod.
The camera's fastest capable shutter speed is 1/1600 sec, however, you cannot set it manually. The camera would use such a fast shutter speed in a very bright outdoor situation (the more light there is outdoors, the faster the shutter speed the camera will select). Using the 'Kids & Pets' scene mode outdoors in good light would also apply a fast shutter speed.
Generally, in lower light you need to use a higher ISO (800, 1600 and higher) in order to get a fast enough handholdable shutter speed to prevent blur. Unfortunately, because your camera has a very small image sensor, means it has VERY poor ISO capability, with ISO 200-400 being the max you would ever want to use (though you will still have plenty of noise at these low ISOs).
You also need to use a very fast lens (one with a wide open aperture) in order to use a faster shutter speed with your higher ISO. The trouble with your compact camera is it's equally tiny and inadequate lens...the more you zoom in, the smaller the aperture becomes...the slower your lens becomes.
So, due to your camera's limitations...your success will be very limited. But, maybe you could try the 'Night Snapshot' scene mode (page 54 of your User Guide) if you can get close to the stage. Though I would expect your image noise levels to be very high.
good luck...