Congrats to your friend on both counts.
ABSOLUTELY DEFER. ABSOLUTELY!!!
If future mommy is 1 month along, she will most likely give birth around July. That would give her roughly one month before starting school, or maybe even less, depending on the school. Unless she is an extremely rare case, there is no way she will be physically or emotionally able to successfully take on a heavy course load just one month after giving birth! For starters, I don't know of any daycare places that will take a child under eight weeks of age. Furthermore, if she's going to breastfeed, we're talking 8-12 times a day around the clock. If you do the math, it literally amounts to an hour or so of "rest" between feedings, and think of everything else that needs to be done -- eating, sleeping, changing, etc. Finally, if she's like most moms (or even dads), being away from baby for any length of time is incredibly hard at first. Most new moms back from maternity leave at my old office were bawling by day 2. Everything settles into a routine, of course, but you just can't miss a day or two of class or study time.
The bottom line is that a newborn sets the schedule of the parents for a few months after birth, and trying to get anything really signifcant done around the same time is very difficult. At two months, maaaaybe with a lot of family support. At one month, no way.
Oh, I'm speaking from experience. I've been a dad for three weeks and two days now. I'll be starting med school next August, and I still don't know just how I'm going to balance everything at that point. Had I been an M1 or M2 this year, I think I would have had to defer; either that or resign myself to being an absentee father when my wife needs me the most.