Healthy Beginnings Act of 1991 - Amends the Public Health Service Act to authorize grants for reducing infant mortality and providing to pregnant women, children under two years old, and the mothers of such children, in medically underserved areas, certain services in the home, including: (1) health care; (2) education regarding parenting skills, tobacco and alcohol use, nonprescription drug use, and family planning; and (3) referrals. Requires that the services be provided, to the extent practicable, through nurses. Allows grants to be expended for outreach. Allows technical assistance to grantees. Authorizes appropriations.