AOL puts down about 600 evil tentacles even if you begin then cancel the installer.
Even if you did install and uninstall QT billions of times, filling your hard-drive, the definition for "worm" you cited would not apply, as self-replication is not a function of the program - it's you who is replicating it.
Uninstall it, delete the folders, search for .ini and .dll files that might be relatd to QT and move them to a folder you can quarantine (in case your PC needs them), and use a registry backup/cleanup tool to get rid of its evil keys.
Then see if anything nasty happens