Every place is different, even districts in the same states have different requirements! Some want you to have ER experience so you know how to handle emergencies, some want only nurses with a special school nursing certification, some will only hire RNs, some will only hire LPNs/LVNs (RN lead), some hire off the bat...it just depends! Not very helpful I know, but true. If you are truly interested, talk to other school nurses, get your "foot in the door" so if a position becomes available you have an "in".
DalekRN has a point about leaving after only 3 months as well. You don't want to appear fickle!
Good luck, feel free to PM me if you have any specific questions....I'm on my 10th year & happy to help