This is actually a very good question. And one that that can help other people. Ah. Refreshing.
To your question...much like any thing in life, it all depends. While it's possible that your dating pool would be limited, it doesn't mean its non-existent. I know plenty of women with children who are dating, and meeting people at an impressive rate. And some of the women have multiple children. It just depends on the type of men you meet and where they are in life and what they're looking for.
Kids don't scare everybody away. I'd wager that most people like children and aren't completely against the idea of dating somebody with a family already. Especially today. It seems like everybody's got a kid. Seriously.
So yes, it will be a dealbreaker for SOME men. Maybe even half. But that still leaves plenty of men who might still date you - once the child gets a little bit bigger. I can't see most men wanting to date a woman who JUST had a kid.
I own a 24 hr childcare facility & have plenty of single moms (with multiple children) who have BF's & fiancés. It's the norm anymore..., don't worry so much.
I wouldn't base a decision of having a child on how my dating life is going to be post-baby. I don't want to come off mean but having a child is a HUGE responsibility. It seems to me that you should be more focused on the best of the child, not your dating life. (ex. being financially secure, stable environment, on good terms with your ex--ideally he would want be a part of this child's life.)
Focus on your child right now. You are about to face a major life change so prepare yourself mentally and financially. In time you will start dating again and you will encounter lots of obstacles. I remember some years ago a nice Italian man reject me when he found out i had a daughter. He told me that he wasn't ready for that milestone. I notice that the older my daughter get that's when they become interested. I also notice that guys would want me but when i tell them that i have a child they go missing in action. I am so happy now that i met a wonderful man who accept me and my daughter and we are looking forward to get married and have another baby.
All i want to say is that don't focus on dating right now but focus on your unborn child. In due time you will find a wonderful man who really want to be with you. You never know what will happen. You might meet a man even during your pregnancy. I know someone who met her husband while being pregnant with another man child. However, prepare for your baby and not date right now.