The Canon G1X has a sensor that is comparable in size to the sensor of a DSLR. This means the camera should perform pretty well on high ISO, noise and in diffraction issues.
The thing is that underwater photography is complex. You really need a strobe and better yet 2. The reason you need strobes is because the water column absorbs the longer wave lengths of light. Below 15', there are no reds unless you supply the light. Farther down oranges, and yellows disappear. At about 70', the world is blue or green. Another advantage of strobes is they tend to reduce the apparent sediment in the water if they are mounted out to the sides.
You can use the Canon housing, but I understand that the housing does not take wet lenses. The Ikelite housing takes macro lenses but not really good wide angle lenses. You want wide angle lenses so you can get up close. The closer your shot the better it will be because there will be less water between you and the subject.
The camera will do you a good job except you will have to be in live few for focusing and composition and that will give you shutter lag. It makes taking photos of small fast moving fish challenging.
Now, a top end housing package with camera and strobes will not be cheap or anything approaching cheap. Be prepared for sticker shock.