If you have iTunes installed then you have QuickTime installed too. You also checked the box that asked if you would like to install the Apple Software updater, when you first installed iTunes. This is an option, not a default.
Your post is a little confusing. Your title is QuickTime alternative and you wanted to know how to stop it asking you to update.
Now it's Apple asking you to update Quicktime which you say you have not go installed.
Now we find it is all happening on a Windows Machine, not a Mac.
Despite the fact that this is NOT Mac software, I'll try to solve your problem.
In your program files, Start/All Programs (for XP) you will find a piece of software called Apple Software Update.
Launch it and let it check for software updates.
Once it has done that, go to preferences and tell it to NEVER check for updates.
Quit the application.
That should do it.
BTW, just because the makers name is Apple, it does not make the software Mac Software.
Office 2008 is written by Microsoft, it does NOT run on Windows.
P