This could be answered in a few ways I think.
As long as he continues to keep his parental rights and chooses for her to stay on, there is no need to worry.
Now, if he chose to take her off, but still has legal parental rights over her, you can actually court order for him to become responsible of the child's health care, that way he'd have no choice but to have her on the insurance.
Also, if he decided to take her off, you can use that against him and he would have to have a darn good reason on why he would take his own daughter off if you took him to court for it.
But I think things should go smoothly and I don't think you have anything to worry about. I just had to throw in those situations because some men, believe it or not, will do that.
Hope everything turns out well for you and your little one :)