http://www.pcmag.com/article2/0,2817,2394587,00.asp?tab=Specs will it run on ultra with a couple of mods??
Koroush Ghazi goes into great detail illustrating the differences between various graphics settings options for Skyrim http://www.geforce.com/optimize/guides/the-elder-scrolls-v-skyrim-tweak-guide/#1
Most of the settings have very little or no impact on frame rate, other than anti aliasing and shadow detail. My graphics card is the 5830m, which is weaker than the 560m in the Asus G74SX in your link. Skyrim runs just fine at 1080p using FXAA instead of regular anti aliasing, but with all the other settings completely maxed. My average frame rate is 40-60 fps, although occasionally it drops below 30 in Markarth. Since the Asus G74SX has a faster graphics card and the display resolution is lower (1600x900), it should run the game faster than my laptop.
Unless there are some specific importation problems in your local market, you should be able to find a laptop under $1000 that can run Skyrim at 1080p (or 1600x900) with most settings maxed except anti aliasing. Also, keep in mind most mods have very little or no impact on frame rate, and if you like a certain graphics mod but it turns out to slow down the frame rate, you can probably find an alternative. As toothman mentions above, however, keep in mind a desktop would be cheaper, of course, and for most laptops you cannot upgrade the graphics card in the future.