Isn't that what AutoComplete (IE), AutoFill (Chrome) (may be named other things in other browsers) is for?
And, maybe, although unlikely, that ISBoxer can help you. ISBoxer is aimed at DirectX applications (and the odd openGL with limits), which browsers generally aren't, and even those that support it, are troublesome.
If it happened to be a Flash browser application, that would work, although still not sure about the virtualisation. You'd need to know a lot about how it stores any local info, and that tends to be in a secure container, which I'm not sure will be able to be redirected (virtualised).
/e I've been re-educated

, and told that Firefox might be able to do what you want if you use the command line arguments to load different profiles, although setting this up via Inner Space/ISBoxer seems overkill when you could just as easily manage this via a CMD file, or a suite of Shortcuts.
Unless you are then wanting to repeat keystrokes or mouse movement, then Inner Space/ISBoxer doesn't really need to come into it; Firefox supports D3D rendering, so it might be possible in the future releases.