You really need to be a bit more precise about what you mean when you say "I want better". For instance, what was "not good" with your Sony? The shots you took in the dark? The noise from high ISO? The contrast? The lack of manual control? the speed at which the camera operates, ie auto-focus?...There are too many variables, of which you don't speak about, in order for someone to give you a relevant advise. You need to be more precise.
One thing that can be said, however, is that you will not be satisfied with a G9.
99.9% of point&shoot cameras - including the Sony and the G9 - share a similar size sensor, which is smaller than a digital SLR. With a smaller sensor comes inherent image quality restrictions, especially when shooting at high ISO. And, unfortunately, the trend for manufacturers is to make compact cameras that are capable of very high ISO, at the (very) detriment of picture quality, because of that smaller sensor, as mentioned earlier.
Probably, the only way you will be able to get "better" quality pictures - at least from a technical perspective and not a creative one - is for you to get a digital SLR. They have larger sensors, are quicker to operate, and have more control than a compact camera.
To start with, you should read a few articles on this website, first of which should be at the beginning of this thread "Should you buy a DSLR or Compact"? Then, you can go to the reviews section and have a read and look at the reviews of various compacts and digital SLRs.
Then, if you decide to get into DSLR, you will have some thinking to do. What is your budget? What interests you? So that you can make an informed decision about which lenses to get. Which features appeal to you, etc.
However, whatever you decide, you should wait, if you can, until the forthcoming photographic show, due very soon, and which will see, no doubt, many new releases in both compacts and DSLR. Unfortunately, choosing a digital camera - if you're a bit more ambitious about your results and don't jump into the first digital compact - demands a bit more thought and time. But if you put some effort into it, you probably will come out at the end with something that will be highly satisfying to you.