If it's a CRT monitor then don't worry - all resolutions look crisp. If it's a TFT monitor, then see how its interpolation implementation holds up. I imagine the picture will be fine for the most part, but text might look a bit ugly (I recommend disabling ClearType in this case).
A video card's maximum resolution used to be a function of the size of its framebuffer (back in the 1990s when video cards only had 2-4MB of RAM which meant a screen size of 1024x768 @ 24bpp (1024*768*3 == 2.25MB). However this is a historical footnote and is of no relevance today.
I read up on the Intel 945 Express chipset and its described as only supporting SVDO and VGA output. SVDO is used for the built-in panel, so VGA is the output port.
1600x1200 sounds like a reasonable maximum for VGA on a laptop - this is because of the quality of the DACs required, and the good-quality circuitry required to drive anything higher. VGA has a maximum ceiling of 1920x1440 which my desktops are capable of - I used to use 21" CRTs and I ran them at 1920x1440 at times - but the signal wasn't really stable enough for quality work, so I ran at 1600x1200 most of the time.
For some reason TFT panels always display worse images of the same analoge VGA signal compared to CRTs - so even if you could force it to 1920x1440 (or 1920x1080) I'm sure you'll find the picture quality abysmal.
So when you do get a VGA monitor that runs at 1920x1080, I'd make it run at 1600x1080 (you can force custom resolutions (below the maximum) by tweaking some files - that way you won't get any pixel scaling and you'll get a reasonably sized workspace. You could try forcing it to run at 1920x1080 but the driver might reject it and fallback to 640x480.
If you'd like a 16:9 workspace regardless, then try disabling interpolation and running in 1:1 pixel mapping on your monitor - but your workspace will be a couple of inches smaller than if you didn't.
Does your laptop have a PCMCIA or PCI-Express card slot? It might be worth getting a card for that which supports higher resolutions (and DVI, instead of VGA). Such as http://sewelldirect.com/vtbookpcmciacard.asp
There are also USB video-cards available - but performance on them isn't great. They're only really useful for office work. They might stutter when it comes to web-browsing too. Your call. (but personally - I'd just replace the laptop. Even low-end