I can answer only in terms of Indiana law, so with that in mind:
It's probably easier to get a divorce. I'm assuming the child is his, correct?
Chances are that the court won't let your divorce be finalized until after the baby is born. And any baby born during the marriage is presumed to be a child of the marriage, unless proven otherwise w/a blood test. Now, this issue definitely varies from state to state. So that might not be the case in your state.
Custody and support issues are considered part of the divorce proceedings and will be decided either by settlement agreement (in which you both agree on the terms and sign off on them, as does the court) or by the court alone after a hearing.
Hope this helps!