I just redeemed an award ticket for my brother with his 2 month-old baby in biz and the standard fare rule for infants travelling with parents on an award ticket is 10% of the cheapest available fare class during the time of travel. My brother have to shell out around U$510 excluding taxes for a round trip between DFW and MNL.

Since you are flying in F, then the $1,000 charge is about right. Forget about insisting on buying an economy fare only as rules are rules. :-)