That's way too much information for your laptop to tell you if you can run something or not, haha. Just simply saying your processor/RAM/OS and a few other things should be sufficient.
From my simple knowledge, I'd guess you could.. But the question really isn't "Can you run Sony Vegas?" but more like "Can you edit and render HD videos easily?".
Just download a 30-day trial from Sony's site and see how well your computer can take it.
http://www.sonycreativesoftware.com/download/trials/vegaspro
Amateur Filmmaker, Machinima.com Director & Partner
