I am a working single mother totally independant with a 3 and…

I am a working single mother totally independant with a 3 and half year old daughter. Her father has 3 - 6 differant jobs a year, so we have had a verbal arrangement with childsupport.
I asked him to move out of my house when our daughter was 9months old in NSW. At the time there was an AVO against him preventing him from drinking for 12 hours prior to seeing us, he was not to be physically or mentally intimidating. The court impossed this for a one year period and it started when our daughter was 5 months old.
He also had a breath alizer installed into his car for 2 years ordered by a court and that was removed a month after our daughter was born.
He did not assist with anything towards IVF, and the first year of her life. In the second year of her life, he gave me a few hundred dollars a month for about 8 months, then it stopped.
Then for the third year of her life he paid a few hundred for a few months and then nothing for 5 months now. I have registered with childsupport but not activated it.

My two questions are: If I activate the childsupport agency to start chasing him for money, will they ever really catch up with him, as he changes jobs so often? My concern is that at the moment he can work in QLD to Perth for a few months each and he has seen my daughter once this year and twice last year. This situation will make him really really angry and I have seen that, it is not nice. I have created a safe environment for my daughter in Melbourne near my family and it is really great. Is it worth it the pain and bearing scared again.
Second question: He has offered to take our daughter for a weekend but she is scared of him and to date I have had 100% care since she was born. How expensive is it to gain full custudy of my daughter, so that he can never have her alone.
On two occassion's he picked her up drunk from childcare and the girls called me because he said he was fine and a big guy. He had a bath with her in very hot water when she was 3 months and 5 months old and continued to drink while in the bath. These two situations have taken me 3 years to get her to sit in the bath without screaming. Her first word was Hot, not mum or dad, she is so worried about hot water. I drove crazy back from the CBD of Sydney to Manly to find these situations and be cool about taking her off him while he was in the bath.
He called last night from QLD Mackay saying that he would have her for a weekend if I liked. I would like to find a way to ensure this will never happen. He has no idea about looking after a child.
One Sunday morning, I was exhausted because I had been up all night with her and she was about 14months old. He said he would look after her while I got a few hours sleep. So he put her in this thing called a jolly jumper which the child learns how to jump and use their feet while hanging in this thing over a doorway. It states that you should only leave the child in this for half an hour. I woke up 3 hours later and she was asleep in it, he had just left her hanging, not changed a nappy, nothing.