A few months back I was looking at buying a Sony R-1. Partly because of the convenience but I was also tired of dust on my sensor. Try as I might it was still a problem. I looked on ebay but decided instead to buy a Olympus E-300. WOW! Is all I can say. I've used Fuji's, Minolta's and Nikon digitals such as the D-70 and the Fuji S-2 but the E-300 is wonderful and usually a bargain on Ebay.
I have two images from it on my profile. The latest is called Pricila.
Yep. But where does the "shaken" dust go? Into the mirror box, where it will be re-attracted to the sensor.
Other companies have tried changing the charge on the sensor and other things. It's just an unfortunate fact of life that dust will accumulate. And you won't see the dust till you've taken the picture. And then you'll have to deal with it all over again.
Here's hoping you have less of it to deal with than with previous cameras. But eventually, you'll need to clean the thing, if only to get the dust out of the box, so it doesn't settle back on the sensor.