I have a laptop & am considering using premiere with a Sony ex-1 with this laptop. It is a 1.8 dual processor & 2 gigs ram. Is that sufficient?
I will be doing only limited projects without a lot of effects. If the system runs a little slow, I'm fine with that. I'm concerned that the system will crash or run very slow. What sort of limitations will I bump up against?

Well it will definitely be slow but the dual core helps. At least it is over the specs :)
My old Dell Latitude D600 with 1.6ghz single core processor and 1gb of ram was able to handle Premiere fine, but then again that was PrPro 2 and low quality video...Just a tip from experience, if you are experiencing slowness/lag I recommend trimming the end of each shot, especially before adding a transition. If you don't the lag may disguise unwanted footage and when you export, you'll end up seeing some other random shot come up, say in the middle of a fade.

just my 2c LOL