Hi Marie,
So you created class, VAT, characteristics, assigned characteristics to class. The you created phrases, phrase sets, and phrase set assignments. That's how I understood it.
After you created the VAT and saved, this action should have prompted the system to ask for a transport, so I guess you assigned one. In the next tep, you should create the appropriate table-based value assignments for your class and manually assign these entries to the very same transport. Then you bring the transport into Q.
The next step is to create a property tree that contains your new class. Export (NOT transport!) this tree and import it into Q via transaction CG35. This will bring the class, characteristics and their assignment into Q.
Later push the transport from Q to P followed by import of the same property tree.
For the phrases, unfortunately they cannot be transported. But you can export/import them including their assignments to phrase sets. The phrase sets themselves have to be set up manually in each system or you do it automatically in TR CGCZ.
Ralph