Well - if you have the drive and know the basic of the job, then you may be onto something.
First thing is first - what are the requirements to be a school nurse in your state? In taking a quick glance at the oasn site, it looks like you need a bachelors and an RN AND a school nurse license. OHIO ASSOCIATION of SCHOOL NURSE
This will require you to go to nursing school AND attain higher education towards school nursing -the good news is that some of your classes from your degree in early ed may cover a few of the classes required.
Nuring school is tough and requires a lot of time and dedication. You can't relive your college days and skip class, as you will miss a lot if you miss class. You will also have to complete clinicals, which are pretty rigorous.
After you finish nursing school, it is advisable for you towork in a hospital to get more experience -remember that as a school nurse, you are essentially alone. You can also work as a school nurse substitute for a while to get a taste of what it's like.
As far as getting a job -it really is dependent of where you live and the demand. Working as a sub may help, as it gets you exposure in the districts.