When you have children your life changes, you must put the needs of that child before anything else
Your daughter does not have to go with you now, she can wait until her child is old enough to make major decisions like moving to the other side of the world for herself
Not named on the birth cert goes in your favour, for now but if dad wants to stay on contact with his child, then it is quite easily sorted in court
Have you actually asked the father about this?
IMO, to take a 16 month old baby, who sees her dad, to another country which is so far away it would be considered impossible to maintain regular contact, is selfish and necessary