I have lived in Oman for the last 7 years whilst working across the GCC so regularly had a taxi guy to do my airport runs as they were not family friendly (hence my missus was sleeping whilst I needed a lift) so I have the contact details of a very reliable guy if anyone needs a quote just DM me.

Regarding the drive there between Muscat and Salalah obviously many people do it, you have two options you can do the scenic route along the coast and take your time but if your short on time as khabah reported it is around 11 hours and it is not that scenic or enjoyable drive tbh. There is loads of rental companies in Salalah and most will allow one way drop off if thats what you want to do in Muscat or vice versa.