You will probably have to get AA to issue the ticket - most carriers ime will require the infant to be issued with the adult and will not issue it standalone
AA will charge 10% of the lowest fare for travel that it can sell - this could easily be a lot more than the operating airline would charge siince many fares have restrictions on who can issue it
Looking at IAD-AMD , EY's fares all have restrictions that mean that AA cannot issue them
The lowest 1 way fare that AA can issue would seem to be $5012.00 for an adult => $501.20 for an infant plus taxes/charges of $24.70 for a total of about $523.90
$700 sounds a bit high for economy class