Its safe by road - no worry's.

If your visa status is good ( i.e engineer or manager ) than you will get the UAE visa on arrival .

you need to Apply for Saudi transit Visa @ 125 QR per person ( documents required are , NOC from the Sponcer , Copy of your Car registration )

and thats it you can go with your family to Dubai in your own car .

Its 700 KM from Doha -till Dubai & very good road