IS IMAGE StABILIZATION THAT IMPORTANT IN A CAMERA?

Image stabilization compensates for camera movement. Instead of getting a camera with image stabilization, get a decent camera and figure out how to hold it still. A cheap, lightweight tripod is fine for such a small camera. If you don't want to spend the money to get a tripod, just put the camera on something like a table and use the self time to take the picture.