How do I get access to purchases older than 18 months ago?

You don't unfortunately. Apple recently changed the TOS with regards to how long they retain users purchase data.

Did you take the Mavericks update and the Pro Key went missing at that time or had it been gone a long time before that?

If you had it up until you updated the OS, there's a chance the preference file with your serial is still hiding on your system. Go into the Library/Preferences folder and look for the com.apple.QuickTime.plist file.

It should have the serial from your QT Pro Key - as long as you didn't reformat when you upgraded, it should still be there.