Sorry, in my experience Firefox 4.0+ versions really need 1GB or more RAM, with a 1GHz or better processor - regardless of what the official recommendation says.

What is your virtual memory setting?

You can check the Virtual Memory settings here: Control Panel > System > Advanced > Performance > Settings (Advanced tab)
If you have less than 1 GB physical memory installed on your computer then if possible add more memory.

• http://support.microsoft.com/kb/2160852 RAM, virtual memory, pagefile, and memory management in Windows

edmeister, Firefox can run on 512mb RAM. I've personally got two computers that do, and plenty of other people I know who work just fine with 512 (or even less, though it isn't optimal).

coldfire, I would suggest trying cor-el's steps above to increase your paging file size. If it is set manually, try setting to system managed.

Another thing you can try doing is starting Firefox up in Safe Mode temporarily. This will help you see if there are add-ons that are interacting poorly with Firefox 12 to create more memory usage. Diagnose Firefox issues using Troubleshoot Mode. If Firefox runs better, start it up in Normal Mode, and try disabling your add-ons one by one.

I see you have the bitdefender quickscan add-on. Try uninstalling it, and instead using something like Microsoft Security Essentials. It's fast, free and light. And IMO, better than pretty much anything else.http://windows.microsoft.com/en-US/windows/products/security-essentials 

Another few things I've heard have helped are doing things such as clearing your list of recent downloads, updating Windows, graphics Drivers, etc.