In Australia, you have to have the Father's permission.  It can be taken through the courts and considering that your other daughter has your last name, it shouldn't take much for them to reach the conclusion to keep it consistant and allow you to change her name too.

I changed my sons names from me ex's to mine.His name was on the birth certificate.But because after a court case he wasn't granted Parental Responsibility and that is how I was able to change it.If he had been granted PR I would've had to ask his permission.

Well, I got my name changed with out my Birth fathers permission. Tho I wasnt in contact with him and hadnt been for a LONG time (but I am now oddly enough!)   Im sure there are steps that need to be taken whether you talk to him or not... but maybe you can talk your baby's father into letting you change her name??   well I wish you the best of luck.

Yes you will need the fathers permission

yes you need both parents names on the birth cert to agree and sign a changing of any name for children under 18. and if the father will not agree and will not sign then you can take it to court and get an order to say he doesnt need to sign. so good luc i hope he agrees its much easier, and cheaper if he does.