assuming you will be driving at 120-140 kms/hr, here is the break down:

- Doha to Abu Dhabi should take you about 7 to 9 hours including border checkpoints (depends on how busy checkpoints are- in weekends they are)

- Abu Dhabi to alain (borders Oman) should take an hour or so.

- Alain to Muscat is about 400 Kilometres. Should take around 4 hours.

IMPORTANT:
there is a very dangerous road once you enter the Omani border. I believe it is near to a place called (nazwa- not sure about the name).

This road is very dangerous and people made horrible accidents there. Oman in general is of a mountain type country and roads are not perfectly plain.

Be careful and have a pleasant trip.