We are licensed for TOAD for Oracle Professional and have the associated Enterprise key.
We are going to develop installation package for the Toad for Oracle Professional Edition.
Are we permitted to create a TOAD for Oracle Base Edition package using that same license key?
A Toad for Oracle Professional key will unlock the Professional edition and features of Toad for Oracle, not the Base edition of Toad for Oracle. Since you mentioned you have an Enterprise key for Toad for Oracle, you may need to reach out to Quest's License Support page to see if and how you might be able to obtain a Base Enterprise key that you can use for your Base installations. I don't know if there are any restrictions associated with that as that's handled by Quest's licensing and legal departments. You can reach Quest's Licensing Assistance page here:
https://support.quest.com/contact-us/licensing
-John