Congratulations on the job offer!!!...they apparently liked your interview, I would imagine there where a lot of applicants, so you must have stood out...
This is a big decision for you to make and I would imagine there are some risks that go along with it, painless change only happens in fairy tales

....Can you take a 6 month leave of absence from the school job instead of just flat out quitting??...if you have pretty much maxed out in pay and advancements at the school job that would be a big minus there.... what your doing and making today would be the same in 5 or ten years from now ....would you be giving up a pension or any retirement benefits at the school?....Is the post office job a permanent job with definite advancement opportunities, do they have great benefits and a retirement package?....
Fear of the unknown is how some great things start....sometimes growing requires us to getting out of our comfort zone....Good luck with your final decision....