Keep dry, cortisone. Since you can't stop a baby from drooling, keeping the skin dry with frequent bib changes is the best prevention. The rash is a form of contact dermatitis and can be safely and easily treated with twice a day cortisone cream for 1 week. If this does not help, please have the rash checked by your pediatrician.
Pat dry and protect. It can be tough to keep those cheeks and chin dry when your baby is drooling it up. Keep her cheeks and chin as dry as possible during the day by periodically pat drying. Clean the affected area 2-3 times per day with a warm washcloth and pat dry. Apply a gentle emollient cream containing lanolin to protect those areas, especially before nap and bedtimes.