Should I?

This afternoon I was checking out the job listings for the area we are moving to soon.  We've lived there before and I worked as a substitute, so I wanted to see what the listings were looking like for the school district.  I would really like to be a teacher, but I came across another job posting that would be perfect for me.  It is for a military family liaison in one of the elementary schools.  The position basically entails working with military families to make their transitions from place to place as smooth as possible for the students.  It requires knowledge and understanding of military transitional life, etc.  Duh, I'm perfect for that job!  Basically, it takes my life experience and my passion for working to ensure that kids get the best educational experience they can and melds them together.  Here's the problem: the application deadline is at the end of this month and we won't be there until after the first of April.  I really really want this job, but I can't start until mid-April.  Should I apply anyways and explain my situation in the letter of intent?  Or should I be totally bummed and let it go?  I'm so torn...