I had a baby at the end of my 2nd year (not planned). It was very challenging, but ultimately, I got through it and I'm glad it happened when it did. He is 18 months now, and things are easier. Those first few months were rough. I would say that the feasibility of having a child in graduate school depends on several factors:
1) Health insurance: Will your program cover your baby after s/he is born? How good is your maternity care? This may seem like a non-issue with an easy birth, but my son was premature and the medical bills were $100k for a 12-day NICU stay. I paid nothing thanks to good insurance, but it would have been devastating if that wasn't the case.
2) Child care: Grandmas and great aunts watch my son for free. Child care in my area is $700-$900/month for full-time care, which is more than I can afford as a grad student. Daycare hours also aren't always conducive to late prac/study nights either.
3) Time off from school: I had only 2 weeks off from class, and it was tough. I made the decision to do it rather than delay a year. If you can time the delivery for summer or afford to push things back a semester, do it. The difference between going back to a regular job and going back to grad school is that school/prac/research responsibilities don't end when you go home at night (at least for me). I'm usually working on something throughout the week and on the weekends.
4) Support from your advisors, professors, supervisors, and PARTNER: This will make or break it, in my opinion. I generally had a lot of support from supervisors (taking breaks to pump, cutting me some slack after the birth), but some were not so helpful (e.g., not providing a place for me to pump). Institutions legally have to provide accommodations, but that's not always the reality. I cannot say enough about the support my husband provided! I would not have made it through emotionally without him. I had the idea that I'd just do schoolwork while the baby napped, or take him to the park and do my reading....and sometimes it worked out this way. But most of the time, it was more like, "babe, can you please watch the baby for 2 hours so I can go to Starbucks and write this paper - otherwise it's not happening." And he was there for me in those moments. It has to be a team effort.
5) Your coping style: Can you handle a lot of stress? Are you organized? Can you function on 4 hours of sleep for 3 months while in school? Having a baby in grad school requires a sort of burning desire to persevere--at least in the beginning. If you are the type of person that has that internal drive, then it can be done.
These are just the top things that come to mind. Obviously this is just based off my own experiences. I understand not wanting to wait - and I think it can be done if you have good planning, good care for the baby that you can afford, and tremendous support. If that's not possible now, I'd wait until postdoc. But regardless of when we decide to have children, it's always so hard as a professional parent! It's really hard to leave my baby every day, but I can't imagine my life without my work. That wouldn't have changed if I had my baby today, next year, or 5 years from now. And of course, I love him more than anything in the world!
I am glad these discussions are happening so we can support each other!
Good luck
