Can I get into legal trouble if I leave the country with my daughter?

I believe you now need to have both parents' consent in order to get a pport for a minor. As long as you have a pport for your daughter, no one will ask you where the father is. I have travelled abroad with my two children and it's never been an issue. Once you leave and stay in the other country, your daughter's father may pursue legal chanels to try and get visitation with his daughter. You'll deal with this if/when it happens.