Yeah, sounds like your computer has pretty much the same specs as mine, with the possibility of a slightly faster graphics card. You should be able to do 1080p editing, but it's likely to be a bit clunky.
I assume you're using a Windows computer? If so, I can't really help you out any more. I'm a Mac Final Cut Pro/Avid editor, I know nothing about Sony Vegas or other similar Windows-based editors.