Well, you're probably gonna have trouble upgrading a laptop because most laptops are build around specific hardware and they make it hard or impossible for you to change or upgrade that hardware. Anyway... a desktop is always better to play games, especially games like FSX. And it's much easier to get parts for and to upgrade.
Unless you have my laptop.
Anyway knowing this laptop by heart because I have sold / worked on so many, I can tell you that there is absolutely no way to upgrade the graphics, sorry but its built into the chipset. Your best hope for upgrades would be 3GB of DDR2-667 RAM and a AMD Turion TL-60 (unfortunately you can't buy OEM TL-64s yet). This upgrade would cost you give or take $350 (which I'm guessing is about $75 short of what you paid for the notebook after the rebates) and totally voids your warranty. Not to mention that this may only gain you a few frames more and the ability to have a bit more AI but overall almost no real graphical change.
Also your comment about your desktop is a bit flawed. If you set your rig up right most people can't tell the difference between AMD and Intel unless they are benchmarking or encoding. So depending on what you have in your desktop you most likely have a better simming rig there anyway.
My overall recomendation is at the very least put 2GB of RAM into your laptop. Its an $80 upgrade, and if you are worried about voiding the warranty you can bring it to a local repair shop that is HP certified. At the very least you will actually have full use of your lappy as you aren't going to be using your page file, and thus everything speeds up, and you don't want to tear your hair out as much.
Cheers
Cameron
EDIT: I just saw that you are in Australia. If this is true, your cost of parts just sky rocketed. Doing the RAM and processor would actually cost more than you spent on the laptop itself.