Since you got single ticket, Airlink and DL do have interline agreement and your baggage will be checked through. In other words its not possible to have single ticket and not to have your luggage transferred (with few exceptions like INTL-INTL connections in USA etc where you have to clear through customs, but your bags are still tagged all the way). The bag allowance and fees will be determined by DL ticket / DL status.

Airlink is a good airline, do not worry and enjoy your trip to SA.