Congratulations Dawndae, 1) on your new 'addition', and 2) on your upcoming 'new addition' to the family.
Well, I'm a big fan of pocket doors when it comes to needing a door in a small 'space'. It sounds as though your husband is handy enough that he could do this himself. (For some useful info, check out this recent post - Pocket Door Links.)
BUT, in a much broader sense, you could go to the other extreme and hang a curtain to create the privacy you want. Understandably, I know you aren't going to do the latter but the point I'd like to make is not so much what you're going to install for privacy but will it be QUIET enough with whatever you install? I have to tell you that we have a pocket door between our family room and dining room. It's extremely quiet, almost like the 'party' in the 'other room' isn't there. But, we also have carpeting on the floor. Before we installed the carpeting, it wasn't as quiet. And since the carpeting was installed (in both rooms), it's VERY quiet. I guess all I'm saying is that sound will travel, even under a door, if you aren't prepared to 'block/deflect' it. And if you and/or the baby and/or your husband want some quiet, it may not be as quiet as you want.
In short, I vote for a pocket door but you need to consider how else unwanted 'sound' will enter the room. (IE., under the door, through the outside window even if it's shut, the closet, etc., etc..) My best to ya and hope this helps. I'm sure others will add their thoughts.