As far as a dual-core netbook, I know of at least one - the Sylvania G. Not a well known one as yet, but it shows up as dual core under Windows.
I would really think about how you are planning to use a netbook. The sub $300 ones that I have looked at so far compromise so much on the keyboard that it is difficult for regular touch typing.
On my G, there is no right shift, ctl or alt and the keys are tiny. I have had to use a modified typing style (cross between two-finger and regular two-handed) and it works ok - I wouldn't type out any big emails or Word documents on it. Very easy to hit the wrong key, etc.
As far as battery life, on mine, I get about 4 hours with using the wireless, installing software, etc. - all tasks that are more demanding on the processor and battery. Most ones in this price range will give you 3-4 hours. Of course, more notebooks are starting to get this kind of battery life (some even get 6-7 hours of real-world usage).
So, while the small size is great, I think you would be happier with one that costs a little more (> $300) to get a decent keyboard and more battery life (some are getting 8+ hours of real-world usage).
Just my 2 cents.