I would strongly advise against this. As you know, Qatar and Saudi Arabia are still embroiled in a quasi cold war and there is always a chance of things getting a bit more tensed at a given point in time even though this is not the current trend. Your chances of getting your bp for the ex-DOH flight are about zero, and even bag through checking on a single ticket on multiple airlines, and multi segments including one ex-doh are 1) uncertain, 2) quite like to lead to something going wrong and your having to chase a lost bag fr days, which doesn't sound ideal on a round the world trip.

I assume you have strong family, business or religious reasons to want to visit Saudi Arabia, as mentioned by makrom, tourist visas are almost impossible to get and whether worth the trouble is certainly open to debate...