Go to AA.Com, click Travel Information, on the Left side, then click Travel Assistance - there are all the information you need to know for Elderly, Disable, and Children travel alone.
For the clarification sake I am copying the Children section below :
THE FEE PORTION IS AT THE LAST PART OF THIS POST.
5 through 7 years Children 5 through 7 years of age must travel with another passenger at least 15 years of age or they will be considered Unaccompanied Minors. See Children Traveling Alone for more details.
Unaccompanied Minors in this age range may only travel on flights not requiring a change of aircraft. They also cannot travel alone on certain American Connection flights operated with aircraft not requiring a flight attendant.
Specific information may be obtained through AA Reservations representatives, or at any American Airlines ticket location.
Fares :
Fares
International (outside the United States/Canada and Hawaii/Puerto Rico/U.S. Virgin Islands)
For fare purposes...
an infant is defined as a passenger under 2 years of age
a child is defined as a passenger 2-11 years of age.
Availability of fares for infants and children varies depending on your travel plans. For more information regarding fares for children and infants traveling internationally, please contact Reservations.
Fees For Unaccompanied Minors
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NOTE: The fees listed below are in addition to the applicable airfare.
Children who will be traveling alone within the United States, between the United States and Canada or between the United States or Canada and Puerto Rico or the U.S. Virgin Islands will be required to use the Unaccompanied Minor service subject to the following fees:
$40 each way for nonstop or same plane service
$75 each way for itineraries that include connecting segments
Children who will be traveling alone outside of the United States will be required to use the Unaccompanied Minor service subject to the following fees:
$60 each way for nonstop/direct flights to/from Mexico, Central and South America, the Caribbean (including Jamaica) and TransAtlantic/TransPacific flights
$90 each way connecting flights to/from Mexico, Central and South America and the Caribbean (including Jamaica) and for itineraries that include connecting segments on TransAtlantic/TransPacific flights
Please also note the following:
Effective with bookings made and tickets purchased on June 15, 2005 or later, the charge for all Unaccompanied Minor services - on nonstop, through or connection flights - will be $60 USD each way for all domestic and international travel.
The Unaccompanied Minor fees for TransAtlantic/TransPacific travel apply to all customers.
When two or more children are booked and/or ticketed and traveling together, only one fee applies each way.