Hi Whatanight
Well done for making the break it is very hard to do but for your DD you have done the best thing for her future.
I work with a lot of women who have been through similar situations to you
I find that the children tend to adapt very quickly.
One of the things I would stress is to not talk about his bad behaviour in her hearing. THis is something that I come across time and again and think can be pretty damaging to hear your dad being slagged off, in code or not
Also think very carefully about any access visits he has. As his behaviour sounds erratic he may do something to harm your dd to get to you. DOn't want to sound scaremongering but I have experienced this in the worst scenario possible by a father who was said to love the ground his kids walked on.
aorry to dwell on the negative
the positives are far bigger though, means you can get on with you live with your dd in a safe and happy environment
I really hope things get better in the new year ans wish you all the best