If it were me, I'd take the baby as a lap baby in business class and let the nanny fly solo in economy. BUT my kid is very happy to curl up in my arms and fall asleep.
What time is your flight and how is your child's night sleep? Could you do a red-eye and have her in a carseat back with the nanny? Would she sleep a long stretch?
And I've always nursed my son in my seat--I'm not sure where else I would do it? Or why? And I certainly wouldn't use formula for a breastfed 11 month old just because I was flying. First off, it's a hassle, and second, lots of older babies don't particularly care for it. And, like, a million other reasons ...