T.P.
I traveled alone with my 6m old daughter and had no trouble at all as far as needing Dad's permission. It is actually not nearly as difficult to travel by plane with an infant as it will be once they become a toddler. Just make sure on takeoff and landing that your baby is hungry enough to be interested in nursing, as the sucking motions help equalize their little ears. At that age as long as they are with Mom and have a meal handy, they are pretty much secure and happy.
I would suggest bringing her birth certificate or a copy of it just in case. On one trip they did not ask for it, but on one trip they did. I always figure better have it and not need it than need it and not have it.