In addition, there should be and additional 'Library' folder for each user account folder. This 'Library' is available for use by all accounts available on your start-up system.
There should also be a 'Library' folder at the root level of your start-up drive. One is located in your 'System' folder and should contain Apple components like the QT MPEG-2 component if you have purchased and installed it. Which 'Library' folder are you looking in? Basically, there can be a number of 'Library' folders. I don't see a Quicktime folder in Library on my computer.