I have been there, exactly. I found out I was pregnant on the second day of R2 year (in surgery) and it was equally unplanned. For all the smug idiots out there, there is an enormous difference between accepting theoretically a risk that heterosexual sex leads to babies versus actively attempting to conceive one.
Firstly, what specialty is your husband in? The flexibility or lack thereof of his schedule will make all the difference. My husband is a corporate litigator gone for weeks at a time at trials, so that colored my experience. My surgical friends who had babies in residency were married to: 1) a house-husband; 2) attendings x 3; 3) a medicine resident [they were able to arrange their call so they were never on on the same night]; 4) a work-at-home realtor; 5) an engineer with banker's hours; 6) a banker with banker's hours. Most of them had family in the area-- and many of the attendings had live-in help. So they had dramatically better experiences.
Secondly, accept the fact right now that once your 28d maternity leave is up (which is what the Surgery RRC allows-- your program might give you 6 weeks, but you will have to make up the extra 2 weeks in the future by either graduating 2 weeks late or giving up all of your vacation one year) that you will, at most, be providing approximately 5-10% of the child care. You will need to make some kind of formal-- likely commercial-- arrangement to cover the other 90-95%. Surgical schedules are absolutely not conducive to regular daycares, which at best are only open for 12 hours a day and never on weekends or holidays. Nannies are usually contractually limited to working a total of 50 hours a week. Again, depending on your husband's flexibility and the availability of family member to provide *routine, reliable, free* child care, you should expect at minimum to pay for both daycare and an early morning/evening/weekend nanny. This is very expensive (I was paying $3500/month, 100% of my salary). If your husband & family are able to shoulder the load, wonderful-- just accept the fact that your bonding with the baby will be on your golden weekends, and in the evenings after s/he sleeps and in the AM before s/he awakens.
Thirdly, obviously you will work up until the day the baby is born, barring medical complications of pregnancy. The only modifications to your duties you need are being excused from the OR during fluoro procedures when you're on vascular. Personally at the very end of pregnancy I found being in the OR very difficult, physically-- it was difficult to approach the table and the heat from the bair hugger would vasodilate everything in the abdomen which made me quite light-headed. But as in intern in an academic program, that's less of a concern. 🙂
Fourthly-- by all means, take your research time early. Since you mentioned you're in an academic program, I assume you're looking at 5+2. If your program is remotely flexible, you could even consider going out into the lab after your first year. Since your baby is due in April, you'll go back after mat leave in May, and you'll only have 8 weeks max to scramble for child care before you go out into the regular banker's hours lab time. Might be a godsend.
You are not the first person to make it work, but please do not think that it's easy, and please do not think that residents in other specialties' experiences are remotely applicable to yours. You will find yourself in horrible zero-sum Catch-22s all the time-- fun things like "it's 6:30, my daycare is closing in 10min, if I don't pick up my child they call CPS at 7, but my patient is coding and night float isn't here yet." It's not PC to say this but it's true: you will be a worse resident because you have a kid. Is it worth it? I definitely think so, and I'm extremely grateful for my happy little accident.