My first piece of advice is that there is never a "good" time to get pregnant and/or have a baby!
You will always not have enough money, not have enough time, not have enough energy, wanted to do something else, etc... So be careful about any "reasons" (excuses) for not starting a family--look closely at them to see if they really and truly get in the way. That said, there are certainly times when it's more opportune or less convenient to have a baby, so trying to plan is always a good thing--I like to have life planned out, in general, anyway (my husband and I have a 10 year plan/timeline that we wrote out).
I had my first child the summer between my junior and senior years of undergraduate. He was a surprise for my husband and I. We hadn't planned on starting a family until we were both done with undergraduate (my husband was still in school at the time as well). But, of course, we rolled with it, and I actually think my son might be better off for having spent his younger years watching us study our butts off (he's 6 and likes looking at text books and watching lecture videos...LOL!)
. It was difficult, but not too hard. We couldn't put as much time into extracurriculars (but I did take him with me to club meetings and activities, and both my husband and I took him to class a couple of times, because we had no other childcare--we planned our classes such that one of us could always take care of him, but tests outside of regular hours caused some issues with that plan), and we couldn't just go hang out with friends until midnight (we weren't partiers, so we weren't affected there). But it all worked out wonderfully, I think. We planned our second baby, and our third was another surprise. So, just be careful thinking that you can carefully plan out baby creation, LOL. It doesn't always work so perfectly--with both babies coming when you didn't expect them too, and the possible fertility issues that are more common as you get older.
I'm not a big fan of fear-mongering about pregnancy complications. Most pregnancies in healthy women who take care of themselves, eat right, and exercise are uneventful. But, it is important that you are taking good care of yourself. So, given my experience, anytime it's possible that you could get pregnant, and especially if you are in a stressful environment, like school (and especially vet school), take really good care of yourself (by eating as well as you can manage, taking vitamins/supplements, and making exercise a habit) and if/when you do get pregnant, you'll be more likely to have a smooth and uneventful pregnancy and birth.
Remember that during pregnancy, you'll be tired and have less energy. And sleep will be important for not only your baby's development, but for you to function properly. And caffeine is a debated topic...some people cut it out while others don't (personally, with my first, while I was in college, I cut out caffeine, cold...with my second, I had none in the beginning and some later on...and with my third, I had small amounts when I thought it was really necessary throughout...).
In general, having a daily plan and a schedule is important. If you don't, you simply won't get things done. Kids, even as babies, suck up a lot of time (and so does housework...and if you're not careful, the internet). This is important all the time, but I'm finding it imperative right now as I'm preparing/trying to get in.
If you do decide to have a baby before or during vet school, have a plan for what you guys will do...but, mentally, leave flexibility in that plan. We have made our plan, but it's possible that it will change if that becomes necessary or best for our family. As of right now, my husband and my kids will not be moving with me to vet school. My husband is in the Marine Corps reserves and is on his second deployment (since we've had kids), so we're basically just going to switch places/roles a bit (which I know happens in dual-military families all the time). My husband has a good job and we have a house, and I'm applying to vet schools within the region so that I can use commuter rail/trains or commuter flights to get back and forth, if it's not an easily drivable distance. If he deploys again while I am still in school, my kids and a nanny will simply come live with me. Of course, it won't be as simple as "simply"...it will involve moving making sure my place I'm renting is big enough, moving all their stuff, and changing schools, and then being the primary parent again. But it can be done, and won't be that much different from what we're already sort of used to.