I would suggest putting your camera on a tripod, use aperture priority and setting the lowest, a medium, and a high aperture allowing the camera to choose the shutter, and shoot at each ISO so you could compare. Do it inside the house where you won't have a lot of light and some good shadows to look at the noise.
I shoot my bridge camera up to ISO400. 400 isn't ideal and there is a lot of noise, but I can get rid of it in Photoshop to my liking. I understand that I'm not going to get the greatest of image quality out of my camera, so I have to compromise my expectations with the limits of my camera. A little noise is fine, I mostly print 4x6 shots or reduce to 800x533 for the web.
Any dSLR I would expect to have much better noise control than my (similar to the one you mention) camera. I see photos all the time posted here with someone mentioning or complaining about the noise and I look at it pondering where the noise is. I wouldn't expect any dSLR to be as noisy at ISO 1600 as mine is at 400, so I would expect to be perfectly happy with any 1600 shot from a dSLR.