No, I'm sorry. You cannot upgrade the graphics on this laptop. The only laptop I know of, that has a graphics card that you can remove, and upgrade is an Asus C90s.
Edit: The 8600M GT is Integrated graphics. This means it's SOLDERED to the motherboard.You can't just go out, and buy it. It either comes with the laptop, (Integrated), or it doesn't!
http://www.nvidia.com/object/wtb_notebooks.html#eightSeries
http://www.notebookreview.com/default.asp?newsID=3881
Asus C90s.
1.http://www.youtube.com/watch?v=kPrw89QIXic
2.http://forum.notebookreview.com/showthread.php?t=142447
3.http://www.directron.com/asusc90s.html
4.http://www.directron.com/90c1ciz5jxbn0.html
5.http://www.zipzoomfly.com/jsp/ProductDetail.jsp?ProductCode=80860&prodlist=celebros (Example: Out of Stock at this site)
6.http://computershopper.com/feature/build-your-own-laptop-200804-2
(Will support up to an Intel Core2 Duo Extreme Edition X6800, {DESKTOP processor!} Will support up to 3GB's of 667MHz DDR2 ram. At the site above you can get the barebones Asus C90s with a 320GB Sata harddrive!
Just wanted to show you that there IS a laptop you can change the graphics on. This is because it has a dedicated graphics card like a desktop computer)
Edit 2: Nvidia has come out with MXM graphics technology. They are trying to make it so laptops can use an external graphics card, but are internal at the moment. The laptop must support it, and again, yours doesn't.
http://en.wikipedia.org/wiki/MXM