The employment question is really a how long is a piece of string question- especially depending on where you live. I work for the Dept of Ed in WA, I have been teaching for 7 years now, and have never really be without work- however having said that I have never had a permenant job, each year I am on an end dated contract, so come the end of the school year, I am never sure if/where I will be teaching the next year. Each state does things differently, here the schools are staffed through central office, so you put in your application for the schools/ year levels etc that you are qualified to teach, and they match you against available jobs- we are just moving into Independent Public Schools, where teachers can apply directly to and be hired at school level, rather than having to go through central staff.
There is a ranking system for placement of teachers- unplaced permenant staff, permanent staff transfering, fixed term teachers & then graduate and re entry teachers. There are alot of teachers struggling to get full time and on going employment, especially if they are not willing to go and do a country stint. I have only just gained my permenancy this year after 7 years of teaching- 2 years in the country and 5 years metro, I got my permenancy through spending 2 years in a "difficult to staff school" in the metro area.

As for qualifications- Generally High school teachers have a specialty and do a teaching degree, either a bachelor of Ed high school, with units in which ever area of study they are interested in, maths, science etc. Or do their specialty degree then a Grad Dip in Education.
Primary school Teaching is another seperate degree- a 4 year degree in teaching (in WA) this means you are qualified to teacher years 1-7
Then there is an Early Childhood Degree- also 4 years and this (once again in WA) qaulifies you to teach k-3.