I have never experienced a OW airline being willing to reissue another's RTW without a reason. Merely asking for a reissue without some ostensible need is not sufficient.
However, there are a large number of reasons/situations that will prompt a reissue. Assuming you have QR flights in the itinerary, QR will likely reissue if there is a schedule change, date or time change on their part or if you request a date or time change from them. A route change request from you to QR involving QF flites will almost certainly result in a reissue. Note that in this case a change fee may apply. Some agents may be reluctant or uncertain about the extra work involved, so HUCA may be needed.
Why is it important to you to have the ticket reissued? I'm guessing it is to use QR miles for some type of upgrade, but this is not clear from your post. Perhaps if you made that request/reason known to QR they would be willing to reissue as part of granting your request.