I worked labor and delivery for 10 years and unfortunately, tragic things happen, thankfully not often. I remember having that same thought about being a Wal-mart greeter :) We are nurses because we care so much and put our hearts into caring for our patients and it takes time to process and heal ourselves when something sad occurs. While it does sound like staffing on your unit needs to be much better, and I don't know all the details, this sounds like an event that probably couldn't have been anticipated or prevented. Yet, because we do care we revisit the incident trying to understand. If you can, try to think about all the special experiences you helped families with--you never get tired of the miracle of birth. I agree with the previous comments to take some time to think about a move but if the staffing is not improved you might consider a new place. If you have the strength, with time you might rally to improve the staffing on your unit.
Wishing you peace in whatever you decide to do.