Try kayak for comparisons with other airlines. It seems to come up in the $1000-1200 range one way for the adult only, not sure what surcharges there would be for a lap infant.

I'd suggest you phone BA and explain the circumstances and see if they can change the award booking for a reasonable fee. Hopefully you could find someone to help you work it out.

I hope the little girl is feeling better. Good luck with it all.