Founded in 1976, Davidsonville Pediatrics is surely one of the most unique and inviting pediatric offices in Maryland. You'll love our award-winning staff. During your visit keep an eye out for peacocks, cows and chickens! 2772 Rutland Road, Davidsonville, MD 21035 (410) 721-2273. Hours (Until Further Notice): Monday-Friday: 7:30 AM - 5:00 PM.