There is no Pro version of QuickTime X. By default, QuickTime 7 is not installed in Snow Leopard, you must choose it as an option. QT 7 is the one you apply your Pro info on.
To install it after the fact, you can insert the second gray disk your Mac came with and double click the extras installer package. Then choose QT 7. Or, just download QT 7 from Apple.
Once installed, launch QT 7 (it will be in the /Applications/Utilities/ folder). Go to the preferences and enter your Pro activation data.
Note though that this will not do a thing to help stuttering on playback. The Pro activation allows you to save QuickTime movies and other features that the player alone will not do.
Yes, you need QT7 NOT QT-X.
Once you have 7 installed, click on it in the Menu bar, and there will be an option in the drop-down for registration. Add in your reg key, and hit TAB at the end of your code. You should then see PRO show up under the QT icon.
Be aware, that you will STILL have to QUIT quicktime, and then re-open it for the unlocked features to become unlocked after this.