Such a thing does exist, but if you post it on Qatar Living you won't get the best response, since UK, USA, western etc people with an RP for Qatar get some sort of visa waiver when they travel to Oman.

I'm not sure where you could go to get info on this. Perhaps try contacting the Oman Air or Qatar Airways offices in the UK, or even the Qatar embassy.

Perhaps a good travel agent could provide some advice?