Hi,
You created release strategy and it is working fine in development system.Now you transport TR to quality but release not triggers for PR.
As you have PR document type ZDOM only in quality system, so keep value PR document type as ZDOM in Release characteristics of PR document type in quality system( you have different PR document type in Release characteristics of PR document type in development system). If the value ZDOM available in Release characteristics of PR document type, then you can enter the ZDOM value in t.code:CL20N with PR release strategy,PR release group and PR release class.
Now create a new PR with ZDOM PR document type and see how release strategy triggering!
Regards,
Biju K