Janet,
The size of the dog doesn't matter, in fact more people are bitten by smaller dogs than the larger breeds. More are bitten by their own dogs, but any bite to the face is potentially dangerous because of infection and infants would be more in danger than an adult. Yes it does say something about his responsibility but viscious dogs are put down every day. BTW, the ball of fluff dogs are "chick bait".
If you can get him to provide his DNA, both of you go to the lab so the chain of custody is not violated and you know it is his DNA, before he leaves by all means do so, however, don't sign anything. He can sign if he want's to, but you wait until the baby is born unless you have some reason to have amnio before birth, then the baby's DNA can be tested at that time. Then file for child support, let him worry about filing for custody and visitation. When you file for support, have it go through The state's Child Support Enforcement agency so your child support will be garnished from his wages rather than him paying or you won't see any, don't forget to ask for medical and child care while you work. If you have to file for welfare and/or medicaid while you are pregnant or after, the state will collect Child support from him. Document everything, from the dog bites, abandonment, any threats, his "waiver" his lack of responsibility, financial problems $25K is a pretty big debt. Most likely once he is responsible for child support he will file for custody and visitation, so expect a fight. Since you are just in the learning stages, don't be surprised if his parents don't try to get some visitation. When it comes to visitation there are many options, figure he is going to want to control the situation, so you will need to be prepared beforehand. There can be supervised visitation, he might be required to take parenting or anger management classes, you can ask that his dog not be present, that the child not be removed from the state or x number of miles since he is a flight risk. A lot to think about.
In the mean time, be healthy, try to relax, take care of you and your baby, it is also possible that he will be a changed man once his child becomes a reality, I hope so for the sake of your child.