The 'noise' here is a result of what we call 'hot pixels' on the camera CCD sensor array. This is literally 'hot', i.e. due to increased temperatures, so one way to reduce the impact of this is to take your photos while your camera is physically cool, though this isn't really that effective for extended photo shoots because most cameras heat up pretty quickly.
An alternative method that is very commonly employed (originally by professional astronomers who use digital cameras for their work) is a post-processing trick called 'dark frame subtraction'. Do a search here or on the Net for this term, and you'll probably find more info.
A far more costly option is to invest in a camera with a larger CCD/CMOS sensor, such as the digital interchangeable-lens SLR cameras. These will also tend to perform well at higher ISO settings. However, if you don't need the flexibility of an interchangeable-lens system, I wouldn't suggest going this route (because of the monetary cost) unless you really do a lot of night photography.