dumb idea ?

So I no longer speak to my daughters dad because he has not helped me once through my whole pregnancy he hasn't purchased one thing for my daughter or attended a doctors apt so he basically shows no interest in her so I have cut communication with him to keep my happiness , anyway my worst fear is him trying to take my daughter and get any kind of custody so I was thinking of instead of putting him on child support asking him to just sign his rights over to me so I can move on with my life and never have to worry about him again or is this a dumb idea ? Oh and I'm 32 weeks and 4 days