Panasonic's FZ200, but will the image quality be significantly better than my Canon's, given the limitations of the sensor size?
In low-light conditions, yes. In broad daylight, probably not.
I want a reasonable zoom range (in 35mm terms 24(ish)-600(ish) would be fine. Video ability is important and I want as small a camera as I can get.
If you need low-light performance, the FZ200 is only constant f2.8 aperture superzoom that I know of. But if you don't need low-light performance, you might have a look at Gordon's reviews of:Panasonic TZ40/ZS30Canon SX280Sony HX50V
HTH - Mark