Nope just doing a quick trawl and the CQ is an AMD system while the Asus uses Intel.
Would you could do is look on ebay and look for a compatible Intel chip to fit ..
PPGA478 socket P
Max TDP of 31w
So if you upgrade to the latest BIOS, you should be ok to use a Core 2 Duo T series, aslong as you stick to a FSB 667mhz model.
Just give Asus an email for them to verify.
Found this http://www.pchelpforum.com/xf/threads/upgrade-cpu-laptop.104667/