A few of us have already given you the answer that it MAY be offered at the time of the online check-in (not very likely on a QF award ticket) or you could ask at the airport as they sometimes offer special price upgrade at the airport that can be used for paid-for and redemption ticket. But whether it is offered at all to anyone (regardless of the type of ticket) or not is another matter. This is why no-one can tell you for sure if it will be offered or not.

I strongly doubt BA will let you make any change to the QF award ticket (e.g. paying to upgrade your wife to CE) until 24 hours before departure in any case, if at all. Therefore the options outlined above are the only possibilities, and they might not even be available. There is no certainties and even BA staff members won't be able to tell you for sure whether upgrade options will be offered at all on your flight. Whether to offer airport upgrades are usually decided 24 hours before the flight or the night before, and until then, no-one knows for sure (maybe with the exception of revenue management).

Two things that are almost certain is that BA will not be upgrading her for free to keep you in the same cabin or for extra Qantas points - BA won't be able to touch the QF points, and if QF won't change just one sector which I did not think they would, considering it is part of the RTW (I am very familiar with the QF programme, having been a QF Platinum for about 7 or 8 years, but I thought it might be worth enquiring about just in case they are flexible), the only "realistic" hope you have of having your wife fly CE is by asking at the airport on the day of the flight, or maybe (just maybe) at the time of OLCI.