Upgrading the processor is possible and not too difficult. And fortunately because of the age of our units the price has come down considerably especially for used ones from pulls on eBay. However, don't expect a dramatic performance impact with a faster processor, but rather an incremental one. The biggest impact on perceived performance is and always has been hard drive speed and since you already have a 7200RPM drive that's off the table.
Next would be processor front side bus speed (FSB) because this is the rate at which the processor can access RAM and the other components of the system. The faster the FSB the more quickly data can be accessed with fewer wait states at a given clock speed. FSB has a much more dramatic affect on performance than over all clock speed as clock speed is a ratio of FSB times CPU clock multiplier. You state in your signature that you've got a 1.8ghz processor, so I can only assume you're running a Pentium M 745 running at 400mhz FSB and not a Pentium M 750 running at 533mhz FSB. If this is the case then an upgrade to a faster Processor will yeild improvements provided you not only upgade to a faster CPU, but one with a faster FSB as well. Examples would be a PM 760 (2ghz @ 533 FSB), PM 770 (2.13ghz @ 533FSB), or the fastest available that will fit in your machine a PM 780 (2.26ghz @ 533FSB). You can pick-up one of these PM 780s right now on ebay for as little as $125 (I just did a search there for Pentium M 780). Awesome considering they were over $700 when first introduced over 3 years ago.
In conjunction however, you need to make sure that you're RAM is up to running at this faster speed, otherwise the faster processor will be stuck accessing your RAM at the slower 400mhz bus speed. So my suggestion would be that if you want to go through all of the trouble to upgrade your processor and increase your RAM, that you purchase 2 identical 1gig sticks rated at 533mhz or better (667mhz sticks will run on an I9300, but at a slower 533mhz, this is what I have). This will allow you to run at maximum performance for your chipset and upgraded processor. Since RAM is pretty cheap right now you should be able to upgrade your RAM and processor for under $200 total and prolong the useful life of your rig for another year or two.
If this isn't within your budget then my advice would be to keep what you've got don't sink anything else into it and save your money to buy a newer more up to date rig later.
I hope this helps.