Looking at the specifications of your laptop: http://h10025.www1.hp.com/ewfrf/wc/document?docname=c01781592&tmp_task=prodinfoCategory&lc=en&dlc=en&cc=us&product=3982246&lang=en
and the program that is included with the camera: http://www.pixela.co.jp/oem/canon/e/pixela_application_disc_ver20/spec.html
it looks like your laptop is fairly close to meeting the requirements of that program, with your cpu being borderline in speed.
Editing HD material does take a rather powerful cpu, with most people recommending quad core desktops for this task if you are using a program that can utilize multiple cores.
Two of the better programs for home users would be Adobe Premiere Elements and Sony Vegas Movie Studio, but your laptop doesn't meet their minimum standards for working with HD video. So I don't really have a recommendation for your system. Stick around. Maybe someone else will have a suggestion.
Welcome to the forums anyway.
Edit: Looks like olyteddy beat me to the punch.