This is based on a standard called the International Residential Code. Any habitable residential space must have at least 50% of the space be 7'0" or higher. Although you and your family are short, it is designed to be safe for anyone, including emergency personnel to navigate the room. If your dwelling had a fire and the place was smoke filled, it should be safe for a tall fireman to come in and rescue your child. If your child required emergency support, a tall paramedic should be able to get in carrying equipment and not be in danger from a low ceiling.
The IRC is maintained by the International Code Council and while the name includes "International" it really is a US organization. The ICC standards have been accepted in all 50 states, the District of Columbia and several other US territories. More info at
http://www.iccsafe.org/AboutICC/Pages/default.aspx