If your camcorder does not use FireWire--which Sony calls iLink--and yours does not, then you cannot expect it to be
iMovie-compatible. Apple has a partial list of non-FireWire camcorders that are compatible, but my bet is that yours is simply not compatible. I gather that your camcorder uses a Flash card for storage. I will also go out on a limb and guess that it records in the MPEG2-PS format.
You did not do yourself any favors when you decided that you want to edit video from this camcorder. First, you need to get your video onto your computer. Your camcorder should mount on the Desktop. Open the mounted volume and drag the video files over.
Now you must deal with the MPEG2-PS format. It is a vexation to other Mac users. You may have to spend some money.
Perian does not handle the format. It appears that you need the combination of
MPEG2 Streamclip (free) and the
MPEG2 Playback Component (not free). Of course, you also need
Quicktime Pro.
Certain third-party video converters advertise support for MPEG2-PS. One is
E. M. Total Video Converter for Mac. Its price is $30 US, but can be downloaded before your pay the fee. Hopefully, it has some functionality before you pay the fee.