Not an educational version, but there is a downloadable 14 day demo of QTP you can get from the main HP/Mercury site.
QTP being based on vbs, it shouldn't be too hard to see the basic programming structure of the scripts, and it would give you more than enough time to go through the tutorial and see how the tool's IDE is structured.
Insanity: doing the same thing over and over again and expecting different results
Use the following link (http://msdn2.microsoft.com/en-us/library/ms950396.aspx) to get to the MSDN Scripting page. Go into the VBScript area and have at it. Some of the code examples (specifically calling COM for Excel, and ODBC) will give you a good understanding of what you can do with QTP VBScripting. This is the code I have incorporated into VBS libraries with QTP.
While most of the trial versions are nice to play with. I have found that most vendors will not offer all "extensions" available with the complete package.
I would like to find someplace like an "educational" area that would allow users to "test drive" all applications against each other. Should you find this "heavenly area" please post it for everyones use!