No, it's not possible. Your laptop has a mobile processor using a socket P interface, while the Q9300 is a desktop processor using a LGA 775 socket. They are not interchangeable, plus a desktop chip would get way too hot in a laptop even if it did fit.
Like both of them have mentioned it may be possible, but you can't use a desktop part in your laptop, you would have to use a mobile parts instead. Also of pointed interest here, is the Thermal output of the processor/power requirements of it. The cooling/power systems in the laptop might not even be able to handle the requirements of making the switch to a quad. Also, before you even go looking that far you need to make sure the processor in your laptop is even removable, in some models the processor is soldered right to the mainboard making upgrading the processor completely out of the question. My advice, it will be more of a headache than its worth to upgrade it, get a new laptop, or build a desktop for more performance and use the laptop for just mobility if you really need the extra performance. Good luck
If you want to upgrade to a quad core CPU then you need to search online for the service manual for your laptop model. If your motherboard revision supports quad cores then it shouldn't be a problem as the same heatsink is usually used for both on a laptop. Still, make sure that there isn't a different heatsink/fan assembly just for quadcores because that would mean the dual core assembly wouldn't cut it.
if your motherboard chipset is a 45 series (pm45 , gm45 , gs45) potensially u can , but notice that doing that needs to update your BIOS software to identify your new cpu by motherboard. however after all this u must check 2 more things!
1 : has your system's heat sink harmony with quad core CPUs? as u may know quad cores have two contact with heat sink and they must match exactly with heat sink to make cpu cooler.
2 : after all this if your system has not two separate cooling system i highly recommend that don't do that , however if not u can still do that but running HOT!
notice that TDP (cpu consumption) difference between them is high (25w vs. 45w) . if your cpu temp. is usually about 40 C and under load does not exceed 55 C i think that won't hurt, but if it goes much than 65 C there is some risk to do that.
by the way like the others said Q9300 is not a laptop cpu and cpu u can use are Q9000 (2GHz) and QX9300 (2,53 Xtreme) . i highly recommend QX9300 (if u have budget $1000) as it is very fast and TDPs are not different, but if u want the cheap one Q9000 (for about $350) is the best choice because Q9100 (2.26GHz) has not a good performance/price ratio. good luck . keep in touch if u done that. sorry about that my english language sucks