DON'T DO IT!
The Big Sur drive, Carmel to Morro Bay is one of Natures wonders and fantastically beautiful. That said: Driving South you will be on the ocean, cliff drop off, side, often without a shoulder, drops of more than a few hundred feet, flimsy guard rail...if any, a narrow winding road, with traffic, including trucks coming at you. Going North, you will be on the mountain side of the road, but again no shoulder, and only inches between you and the rocks. There are a few hair pin turns so tight that you can see your own tail-lights (ok, an exaggeration, but the turns are really tight.)
My suggestion: Take 101 to Morro Bay or San Luis Obispo, and base camp there. The 101 drive is lovely. San Luis's Wine Country is great to visit. Make the Big Sur drive a day drive, or even an overnight drive driving North one 1 and driving home South on 101. But don't take a large vehicle on highway 1 South.