xoticpc builds custom Sager laptops and ships worldwide. Amazon didn't work, but this did. I recommend this laptop:
$770 Sager NP5160
i5-2520M
15.6" 1600x900 LED screen
GeForce GT 540M graphics
4GB (2x2GB) 1333MHz DDR3
320GB 7200rpm HDD (other options available)
Built-in Bluetooth
Built-in 2.0MP Camera
http://www.xoticpc.com/sager-np5160-clevo-w150hn-p-2999.html?wconfigure=yes
Unfortunately, shipping is estimated at $159 (I used an HP New Zealand office address to estimate shipping), which will bring you up to about $930, $50 below your limit.
That price was for configuring it with the i5-2520M. The i5-2410M is dual core, hyper-threaded. The 2520M is a true quad core, I think (check wikipedia to verify). I'm not sure which is better between the higher clocked i5-2520M (3.2GHz) and the i7-2630QM (2.9GHz). The i5 will get better battery life and match performance in the vast majority of tasks. I wouldn't upgrade the screen because 1600x900 is pretty good and 1920x1080 will significantly hurt your in-game framerates. Typically, 320GB & 500GB HDDs both use the same architecture from the same manufacturers, just 180GB gets disabled. This is relevant because a 320GB HDD would typically perform just as fast as a 500GB, where as they'd both get outperformed by a 640GB of the same architecture. But I'd still pay the $20 to upgrade to a 500GB.
If you want a 17" laptop, it'll cost you an extra $180 or so:
http://www.xoticpc.com/sager-np5170-clevo-w170hn-p-3000.html?wconfigure=yes
But at least it's got a bit faster video card to go with the 1920x1080 screen. I don't think this is nearly as good of a choice though.