This is not a QuickTime issue so this was not the best forum in which to take up this question, but if you have only Mac OS X 10.4.x on your computer, you cannot install any version of iTunes later than 9.2.1, which you can download here:
Note that you will need to have updated your iMac to Mac OS X 10.4.11.
If you need a newer version of iTunes, you will need to upgrade your system to at least Mac OS X 10.5.8 which would allow you to install iTunes 10.6.3. If you have a new iPhone 5 or iPad that requires iTunes 10.7, you will need Mac OS X 10.6. Neither Mac OS X 10.5 nor 10.6 are a free upgrade.