This camera should work. It is standard AVCHD. You must connect the camera via USB cable, set camera to Play. Camera must be plugged into wall power. Open iMovie, import screen should come up.
Alternatively, you can remove the SDHC card and put the card in a USB attached card reader.
Let iMovie do the import, do not try to move these files in the Finder.
Finally, if iMovie still does not recognize your card, use your camera's menu to format or initialize the card. (You may want to try this with a blank card, because it will wipe out any data on the card.)
If re-formatting works, but you have valuable footage on the original card, you may want to try some 3rd party software like Voltaic HD to try to convert the AVCHD files into Apple Intermediate Codec. Then File/Import the Apple Intermediate Codec files into iMovie.