This is not a very fashionable opinion, but it has been shown over and over again that the optimal scenario for children is to be raised by their two biological parents in a low-conflict, stable household.
Now, obviously, the usual caveats apply - there are lots of family structures and children can do very well in other set-ups; clearly nobody is encouraging (mainly) women to stay in abusive marriages for the sake of the children etc etc (see above point about a low-conflict household). Nevertheless, the overall point still stands.
In this particular case, where the relationship is apparently otherwise good, I cannot see how the OP leaving her child's father in any way benefits her child. Her child would lose everyday contact with their father. In a 50-50 parenting scenario, they would have to shuttle between two families. The parents will almost certainly be financially worse off. In time, the child will probably have to contend with stepparents and blended families, all of which bring challenges of their own. None of this is in the child's best interests.
In my view, the time for ultimatums was before having a child. Splitting up a family is very different from leaving a partner.
Right now I think the OP needs to work on ensuring she is legally protected in the event of a split and focus on the good aspects of her relationship, regardless of the presence of a wedding ring.