Hi MM
is a way to move Transport Requests (not Transports of Copies) from DEV to Q&A system while the Task List still at 'Development without Release' phase
It depends on what kind of correction you are working on.
For Normal Correction:
NO, you cant, As per SAP Standard you can't do this, Original TR not even released during this phase. more over TOC not even created with the phase Dev Without release.
For Urgent Correction
Yes, Urgent correction can be created and released during all the phases except Go Live
refer here Change Request Management scenario: Working examples Development without Release phase
Other options like, you can create TR outside charm and later attach to Task list, but you need to change the SAP_CTS_PROJECT often to achieve this , refer the sap note 1134993 - Checking transport requests outside ChaRM
Hence I could suggest you go for Urgent correction.
Thanks
Jansi