There is simply no guarantee, based on what we saw in the episode, that remaining on the station would have been safer. Kira felt she had to take action to protect her comrades, herself and thereby the baby. Her quarters had just been blown up despite all the security measures that were in place. Prin had already bypassed Starfleet transporter protocols. She decided not to sit around and wait for herself and the baby to be blown up. It's not about pride, but a matter of fighting for survival, or not fighting.
It would've probably taken something major--something, like I said, possibly even on the order of faking her death--but still, I think everything she did in that episode: going there, going there alone, going there while pregnant and endangering someone else's child, was reprehensible. Like I said, had it been her own life, I wouldn't have a problem with it, but she owes it to the O'Briens' child not to subject THEIR son to a risk even more extreme than the one Prin was subjecting her to on-station. And even if there was NO alternative to her going, then she should not have gone alone; at the very least, Odo should've gone, because of all the crewmembers, he could avoid detection and make Prin THINK she was coming alone.