Littlechief, I assume you are using this in automatic mode. If so, the maximum ISO by default is only 800, you can override this to 1600 which should provide for faster shutter speed. This should mittigate the frequency of this occurance, but not completely remove. Another thing you can do is try to compose the image as wide an angle as possible, the lens is much faster at the wide angle than all the way zoomed in.

The best idea, of course, would be to get a fast fixed lens. It will automatically improve your photography lol, just by having so much more potential in the lens. There is a 45mm f/1.8 lens available for the micro four thirds mount which will improve the low-light capability of the camera exponentially.

Changing cameras does nothing for you, as you are running into a problem you will have on all cameras until you change your technique.

*edit - What mode is the IS in? If its turned off, turn it on and apply a 50mm focal range, mode 1. This should give you sharper photos with slower shutter speed.