I don't see a Quicktime folder in Library on my computer.
Which "Library" folder are you looking in? Basically, there can be a number of "Library" folders. 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. There should also be a "Library" folder at the root level of your start-up drive. This "Library" is available for use by all accounts available on your start-up system. In addition, there should be and additional "Library" folder for each user account folder. Components placed in these last folders are local and only available to individual users. Therefore, if you want the component to be available to everyone, place it in the root "Library > QuickTime" folder. If you only want it used locally, then place it in one or more of the user level "Library > Quicktime" folders. If a "QuickTime" folder does not aleady exist at the desired level, then create one -- just be sure to name it correctly.
(Should I?)
Since you say you have already installed the "Flip4Mac" component, you must have a valid "QuickTime" folder somewhere on your drive. Since I have the only user account on my system, I prefer to keep my folder at the root level so it will be availale if there is ever a need to create alternative or special purpose user accounts in the future.
Also, is it the 'disk image' that gets dragged or the other icon?
No, the disk image, when opened, appears to your system as a separate, independent drive device. As such, it allows you to mount or dismount it like any normal hardware device. When mounted, you simply copy the file(s) needed as if you had just pluged in a external hard drive or optical drive. If you already had a root level "Library > QuickTime" folder on your start-up drive, the disk image should create an "alais" QuickTime folder on the disk image. As an alternative to manually dragging and dropping the "Perian.component" to the folder, you could simply drag 'n drop the component to the alias folder and it would have automatically placed it in the appropriate original folder on your start-up drive.