I am planning for the same on July.
1- you must get a terptic form Qatar Automobile Club.
2- Then transit visa to Saudi Arabia.
3- 2 day trip for the 1st day salwa road to Al Hofof - Riyad - Madinah.
2nd day from madinah to Duba, then fast ferry (3 hr) to Hurghada and the to Sokhna then cairo.

The only missing point is from where to book the ferry.