Odds of Getting In
Once your qualifications are met, you should have no problem getting in the door. Getting out is sometimes the problem. There's plenty of opportunity to show your boss that you're worth keeping around and moving up the ladder. To keep yourself marketable, consider putting in some longer hours, weekends, and holidays.
Benjamin Franklin once said that the only three things that are certain are death, taxes and the inability of George Lopez to say anything even remotely funny. (He later revised his statement to include only death and taxes, mostly so as not to alienate George Lopez fans.) Good news for you, Mr. Funeral Director Man (or Mrs. Funeral Director Woman): Death is always in style.
You're getting into a pretty depressing business, so there aren't millions of young, eager students lining up for a job in the field. So, because you have a kind heart, a good head on your shoulders, and a strong stomach, you should have no problem getting your feet wet. Man, that's a lot of body parts to keep track of. Better get used to it.