I have to be the wet blanket here and say this:
If you are going back to work after the baby is born, if no one is going to home all day and the bird will sit in a cage 16 hours a day alone, then I think rehoming it is a good idea, since this would be a bleak and inhumane existance. If you rehome, make sure the person is very knowledgeable and experienced with parrots and can provide what this bird needs.
One of the most highly intelligent of all creatures, parrots need lots of stimulation, playtime and interaction. If you watch them in the wild, they are contantly busy and always with others.
However if you're going to be a stay home mom, then the bird will probably get all the excitement and stimulation it needs just with normal daily activities.