MSP is right. There are no mileage awards for infants. You have to get a paper ticket which is 10% of the cost of the cheapest fare available in your class of service for the award ticket. If you're doing an award in biz the infant ticket can be very pricey. I recently finished a multi-stop transatlantic in biz with an infant and while the adult seats priced in at 100K each plus about $300 in fees and taxes, the infant ticket was over $700!!!

My experience was that I got 10% of the lowest fare, but I had to help the agent find it with a booking code I got from ITA. It was a pretty complicated itinerary so depending on your trip it's worth looking into routing to find both the cheapest award in terms of miles AND revenue price.

Traveling with children makes everything more complicated and award tickets are no exception!