Exporting with original source TC Query?

You don't. That isn't possible. If you have a timeline with many clips...doesn't matter. Any export will include the SEQUENCE code, not the clip code. The only way to export with the clip code is to load each clip into the VIEWER and export from there. But that would be individual clips...you cannot export a single QT file that contains multiple timecodes.

Shane

If you need a paper reference to the clips timecodes from that sequence you can
export and print an EDL. If the sequence is a simple one video track edit, you could also
use the timecode reader filter and create a 'burnt in' timecoded version which will
display the source clip timecodes. This may be of use if you need to track shots back
from your exported master.

Apply filter to each clip, render, export sequence.