One of my female classmates had a baby in the middle of Feb during 3rd year. Never missed a beat. She might have had to make up some exams (idk the details of what she worked out with academic affairs), but she graduated on time with us with no issues. Our schools 3rd year is the lightest academically though, so very school dependent there.
Several of the guys' spouses had babies too during vet school but I'm less impressed by them haha. One had one during 1st year and one during 3rd year. They definitely made it work in terms of having kids and infants at home though. (One of them had 4 kids!) Their spouses did most of the child care responsibilities while school was in session.
There's never a convenient time to have kids imo so just have them whenever and prioritize your life accordingly. Vet school is basically a full time job - 40-50 hours a week of class + studying was was my norm.
You also get a ton of time off throughout the year (winter break + spring break + summer break combined is A LOT of time off compared to an actual job). If you have the ability to control timing to some extent, a summer baby during a break would probably be the easiest just because you'll be off of school from May - August. (School dependent though- some schools go year round, etc).
4th year would probably not be fun/can be brutal sometimes depending on where you go to school or your track, so plan for that. My track was pretty chill because I spent half the year doing public health rotations (M-F 9-5 basically). Our school's small animal trackers had a much worse schedule. If your partner carries the baby it will just not be an enjoyable experience for anyone probably. If you give birth during 4th year you'll probably graduate late.
In terms of missing class for doctors appointments / medical reasons. Meh. I had two surgeries during vet school (1st and 4th year) and had a ton of physical therapy appointments. In my class, the total number of surgeries was at least six - 2 foot/ankle surgeries, 1 knee surgery, and 3 heart surgeries. One of my classmates also legit got hit by a car the day before an exam... our class was reeeal special with medically excused absences. You might have to make up some stuff, but it's very possible to stay on track with course requirements despite needing time off for medical stuff.
Caveat that you should definitely check your school's policies, though. My school was pretty permissive. From comments above, it sounds like tOSU is not that permissive (at least in a specific year). Will probably vary widely from school to school.
Also you need to know yourself to some extent. If you're the type that's gonna be all-consumed, at school and in the library studying like 12 hours a day every day, that's very different than if you're more like me doing 25 hours a week at school and then otherwise just vibing at home.