your camera has an almost instant shutter speed. You just need to understand a few things in order to use it.
First. Most of the delay that you are experiencing isn't due to shutter speed, it's due to Focus time, or Flash.
First, Focus time. Your camera has a two stage shutter button. If you press the button lightly, the camera will adjust the lens focus, and you'll hear a beep when it's ready (this will probably take about a second) Now your camera is ready to shoot. When you press the button fully, the camera will immediately take the picture.
In contrast, If you simply aim the camera, and depress the shutter button fully, the camera will need to focus on your subject and then take the picture (This process can take as long as a second or more) This makes it seem like your shutter speed is slow.
The delay may also be caused by your flash. This will normally happen if you're using "red eye reduction" - This will cause the flash to fire twice, or flash then fire. The light from the first flash causes the blood vessels in the eyes to partially close, and therefore your pictures will have less red eye in them. However, this extra flash takes time. and this will mean that your picture isn't taken immediately.
If you set the flash to "Standard" The flash will fire, and your picture will be taken immediately.
Changing the size of your picture will have no effect on shutter speed, so I would change the size back to the maximum, so you get the best quality pictures possible from your camera.