When in doubt, always feign ignorance...

Don't worry about it now... go to MEL first and then call QR in MEL with the same request. I think MEL office might have a better way of dealing with it than the FRA office can. Don't say that you've asked of this already.. go to the QR office, and then in a non chalant way, ask .. hey I just realised that I have 20 hours in Doha..

If that fails, then do the same in Doha...

During the transit, upon entry to the Premium Terminal, when approached by the Ground staff, ask if a hotel room has been prepared for you. Present them with a copy of the rules on the website... don't argue.

They may be able to arrange something there and then. Maybe. Maybe not. If latter, then ask what sort of arrangements can they give you as you simply 'cannot' stay the day literally holed up at the lounge, no matter how nice it is.

Not every airline will provide STPC - which actually stands for 'Stopover To be Paid by Carrier' on every Business Class fare. Your fare , as you say, is an excellent 'deal' is one of the cheaper fare and hence the STPC may not come with it. The more expensive fare might do.

Very similar to other airlines' offerings of their premier services.. eg Virgin Atlantic's much touted Chauffeur limousine service. The ads make it sound so nice.. but they don't tell you that unless you pay a full fare J class ticket you don't get the car on any other discounted Upper Class fare.

So, you have in effect, saved a bundle on what could have been a more expensive Business Class ticket to Melbourne already. Take heart with that and shrug it off as 'one of those things' that still needs fixing...