There are a few good noise reduction programs out there...so yes, you can deal with the noise.
The 'SLR-like' cameras, like yours, have a lot of the features of SLR cameras, pretty good lenses and decent image quality. However, they use the same sensors as the little cameras. Yours is 1/2.7 " (5.27 x 3.96 mm). Compare that to something like the Rebel XT (22.2 x 14.8 mm)...you will see that the DSLR sensor is much bigger even though it only records twice as many mega pixels. That's why there is much less noise from a DSLR.
I don't mean to belittle your camera or to make you feel bad about your purchase. You can get great images from it. You will just have to deal with the noise.